diff options
| author | dos-reis <gdr@axiomatics.org> | 2013-05-18 05:28:28 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2013-05-18 05:28:28 +0000 |
| commit | 94f0f26e7af32bdb912352f7eb07f0b40f416791 (patch) | |
| tree | 10af29827583376291f696e79104782a214849d5 /src/share/algebra/browse.daase | |
| parent | 90ab94b8d969b3e0af53dc388718869a81fb2dfa (diff) | |
| download | open-axiom-94f0f26e7af32bdb912352f7eb07f0b40f416791.tar.gz | |
* algebra/aggcat.spad.pamphlet: Tidy.
Diffstat (limited to 'src/share/algebra/browse.daase')
| -rw-r--r-- | src/share/algebra/browse.daase | 90 |
1 files changed, 45 insertions, 45 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 52ed26e0..4fa2d1e9 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(1962312 . 3577838827) +(1962302 . 3577843535) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-3997 . T) (-3998 . T)) -((OR (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) +((OR (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -163,7 +163,7 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-3998 . T) (-3997 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -255,7 +255,7 @@ NIL (-81) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) ((-3998 . T) (-3997 . T)) -((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-1014))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-72)))) +((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-1014)))) (-82 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) ((-3992 . T) (-3991 . T)) @@ -339,7 +339,7 @@ NIL (-102) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-3998 . T) (-3997 . T)) -((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-757)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) (|HasCategory| (-101) (QUOTE (-553 (-773)))) (|HasCategory| (-101) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-101) (QUOTE (-757))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) +((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-757)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) (|HasCategory| (-101) (QUOTE (-553 (-773)))) (|HasCategory| (-101) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-101) (QUOTE (-757))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-1014))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) (-103) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -387,7 +387,7 @@ NIL (-114) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-3997 . T) (-3987 . T) (-3998 . T)) -((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-320)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (|HasCategory| (-117) (QUOTE (-320))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) +((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-320)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (|HasCategory| (-117) (QUOTE (-320))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-1014))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (-115 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL @@ -423,7 +423,7 @@ NIL (-123 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasAttribute| |#1| (QUOTE -3997))) +((|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasAttribute| |#1| (QUOTE -3997))) (-124 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL @@ -719,7 +719,7 @@ NIL (-197 -2623 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994)) (-3997 . 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some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL @@ -743,7 +743,7 @@ NIL (-203 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-3998 . T) (-3997 . 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|#3| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasAttribute| |#3| (QUOTE -3994)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-553 (-773)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (-212 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -875,7 +875,7 @@ NIL (-236 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014)))) +((|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72)))) (-237 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,u,v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,u,i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,u,i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) ((-3998 . T)) @@ -935,7 +935,7 @@ NIL (-251 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-3997 . T) (-3998 . T)) -((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (-252) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL @@ -1043,7 +1043,7 @@ NIL (-278 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-3998 . T) (-3997 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-279 S -3094) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,d} from {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL @@ -1223,7 +1223,7 @@ NIL (-323 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014)))) +((|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72)))) (-324 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,v,i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,a,n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} >= \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) ((-3997 . T)) @@ -1543,7 +1543,7 @@ NIL (-403 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) ((-3998 . T) (-3997 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) +((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014)))) (-404 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,b) = product(a1,b) + product(a2,b)}} \\indented{2}{\\spad{product(a,b1+b2) = product(a,b1) + product(a,b2)}} \\indented{2}{\\spad{product(r*a,b) = product(a,r*b) = r*product(a,b)}} \\indented{2}{\\spad{product(a,product(b,c)) = product(product(a,b),c)}}")) (|One| (($) "1 is the identity for \\spad{product}."))) NIL @@ -1591,11 +1591,11 @@ NIL (-415 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-3997 . T) (-3998 . T)) -((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (-416 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-3998 . T) (-3997 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) +((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014)))) (-417) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) ((-3989 . T) (-3995 . T) (-3990 . T) ((-3999 "*") . T) (-3991 . T) (-3992 . T) (-3994 . T)) @@ -1607,7 +1607,7 @@ NIL (-419 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-3997 . T) (-3998 . T)) -((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (-420) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre's book Lie Groups -- Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens, maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens, leftCandidate, rightCandidate, left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,wt,rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight <= \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1619,7 +1619,7 @@ NIL (-422 -2623 S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-3991 |has| |#2| (-962)) (-3992 |has| |#2| (-962)) (-3994 |has| |#2| (-6 -3994)) (-3997 . 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(|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL @@ -1675,7 +1675,7 @@ NIL (-436 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) ((-3998 . T) (-3997 . 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((-3998 . T) (-3997 . T)) @@ -1691,7 +1691,7 @@ NIL (-440 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data."))) ((-3998 . T) (-3997 . T)) -((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-1014))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-72)))) +((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-72))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-1014)))) (-441 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,p(x,y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL @@ -1763,7 +1763,7 @@ NIL (-458 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-3998 . T) (-3997 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-459) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -1891,7 +1891,7 @@ NIL (-490 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-3997 . T) (-3998 . T)) -((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (-491 R -3094) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL @@ -2083,7 +2083,7 @@ NIL (-538 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (QUOTE (-757))) (|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#3| (QUOTE (-1014)))) +((|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (QUOTE (-757))) (|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#3| (QUOTE (-72)))) (-539 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2123,7 +2123,7 @@ NIL (-548 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-3997 . T) (-3998 . T)) -((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) +((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (-549 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL @@ -2219,7 +2219,7 @@ NIL (-572) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-3997 . T) (-3998 . T)) -((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-51) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-554 (-474)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773))))) +((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3862 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-51) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-554 (-474)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (-573 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) ((-3994 OR (-2564 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-496)))) (-3992 . T) (-3991 . T)) @@ -2267,7 +2267,7 @@ NIL (-584 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) ((-3998 . T) (-3997 . 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(|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL @@ -2635,7 +2635,7 @@ NIL (-676 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,ms,number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,ms,number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,ms,number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,ms,number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|unique| (((|List| |#1|) $) "\\spad{unique ms} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) ((-3997 . T) (-3987 . T) (-3998 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-1014)))) (-677 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) ((-3987 . T) (-3998 . T)) @@ -2875,7 +2875,7 @@ NIL (-736 -2623 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. 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differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-3999 "*") |has| |#1| (-146)) (-3990 |has| |#1| (-496)) (-3995 |has| |#1| (-6 -3995)) (-3992 . T) (-3991 . T) (-3994 . T)) @@ -3351,7 +3351,7 @@ NIL (-855 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-3998 . T) (-3997 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-856 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3411,7 +3411,7 @@ NIL (-870 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) ((-3998 . T) (-3997 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-871 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -3623,7 +3623,7 @@ NIL (-923 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (QUOTE (-1014)))) +((|HasAttribute| |#1| (QUOTE -3998)) (|HasCategory| |#2| (QUOTE (-72)))) (-924 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL @@ -3695,7 +3695,7 @@ NIL (-941 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) ((-3998 . T) (-3997 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) +((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014)))) (-942) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) NIL @@ -3767,7 +3767,7 @@ NIL (-959 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a Gcd-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?,info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) ((-3998 . T) (-3997 . T)) -((-12 (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| (-704 |#1| (-774 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-554 (-474)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-774 |#2|) (QUOTE (-320))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72)))) +((-12 (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| (-704 |#1| (-774 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-554 (-474)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-774 |#2|) (QUOTE (-320))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014)))) (-960) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL @@ -3971,7 +3971,7 @@ NIL (-1010 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,b,c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{union(s,t)},{} \\spad{intersect(s,t)},{} \\spad{minus(s,t)},{} \\spad{symmetricDifference(s,t)} is \\spad{O(max(n,m))}} \\indented{2}{\\spad{member(x,t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,t)} and \\spad{remove(x,t)} is \\spad{O(n)}}"))) ((-3997 . T) (-3987 . T) (-3998 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-1011 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL @@ -4039,7 +4039,7 @@ NIL (-1027 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) ((-3991 |has| |#3| (-962)) (-3992 |has| |#3| (-962)) (-3994 |has| |#3| (-6 -3994)) (-3997 . 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(|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-757))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-951 (-485))))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-962))))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (-12 (|HasCategory| |#3| (QUOTE (-581 (-485)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-812 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-485)))) (|HasCategory| |#3| (QUOTE (-1014)))) (-12 (|HasCategory| |#3| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#3| (QUOTE (-1014)))) (|HasAttribute| |#3| (QUOTE -3994)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-962)))) (-12 (|HasCategory| |#3| (QUOTE (-810 (-1091)))) (|HasCategory| |#3| (QUOTE (-962)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (-1028 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,p2)} computes c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4175,7 +4175,7 @@ NIL (-1061 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) ((-3998 . T) (-3997 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) +((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014)))) (-1062) ((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:"))) NIL @@ -4195,7 +4195,7 @@ NIL (-1066 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-3997 . T) (-3998 . T)) -((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (-1067) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For non-fiinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4227,11 +4227,11 @@ NIL (-1074) ((|constructor| (NIL "This is the domain of character strings.")) (|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) ((-3998 . T) (-3997 . T)) -((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-757)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-117) (QUOTE (-757))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) +((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-757)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-117) (QUOTE (-757))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-1014))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (-1075 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-3997 . T) (-3998 . T)) -((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773))))) +((-12 (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3862 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (-1076 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by r: \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -4343,7 +4343,7 @@ NIL (-1103 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-3997 . T) (-3998 . T)) -((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-12 (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3862) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3862 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (-1104 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL @@ -4651,7 +4651,7 @@ NIL (-1180 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-3998 . T) (-3997 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-1014))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-1181 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL @@ -4707,7 +4707,7 @@ NIL (-1194 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{ps} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{bs} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) ((-3998 . T) (-3997 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) +((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-1014)))) (-1195 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.fr)"))) ((-3991 . T) (-3992 . T) (-3994 . T)) @@ -4788,4 +4788,4 @@ NIL NIL NIL NIL -((-3 NIL 1962292 1962297 1962302 1962307) (-2 NIL 1962272 1962277 1962282 1962287) (-1 NIL 1962252 1962257 1962262 1962267) (0 NIL 1962232 1962237 1962242 1962247) (-1210 "ZMOD.spad" 1962041 1962054 1962170 1962227) (-1209 "ZLINDEP.spad" 1961139 1961150 1962031 1962036) (-1208 "ZDSOLVE.spad" 1951100 1951122 1961129 1961134) (-1207 "YSTREAM.spad" 1950595 1950606 1951090 1951095) (-1206 "YDIAGRAM.spad" 1950229 1950238 1950585 1950590) (-1205 "XRPOLY.spad" 1949449 1949469 1950085 1950154) (-1204 "XPR.spad" 1947244 1947257 1949167 1949266) (-1203 "XPOLYC.spad" 1946563 1946579 1947170 1947239) (-1202 "XPOLY.spad" 1946118 1946129 1946419 1946488) (-1201 "XPBWPOLY.spad" 1944589 1944609 1945924 1945993) (-1200 "XFALG.spad" 1941637 1941653 1944515 1944584) (-1199 "XF.spad" 1940100 1940115 1941539 1941632) (-1198 "XF.spad" 1938543 1938560 1939984 1939989) (-1197 "XEXPPKG.spad" 1937802 1937828 1938533 1938538) (-1196 "XDPOLY.spad" 1937416 1937432 1937658 1937727) (-1195 "XALG.spad" 1937084 1937095 1937372 1937411) (-1194 "WUTSET.spad" 1933087 1933104 1936718 1936745) (-1193 "WP.spad" 1932294 1932338 1932945 1933012) (-1192 "WHILEAST.spad" 1932092 1932101 1932284 1932289) (-1191 "WHEREAST.spad" 1931763 1931772 1932082 1932087) (-1190 "WFFINTBS.spad" 1929426 1929448 1931753 1931758) (-1189 "WEIER.spad" 1927648 1927659 1929416 1929421) (-1188 "VSPACE.spad" 1927321 1927332 1927616 1927643) (-1187 "VSPACE.spad" 1927014 1927027 1927311 1927316) (-1186 "VOID.spad" 1926691 1926700 1927004 1927009) (-1185 "VIEWDEF.spad" 1921892 1921901 1926681 1926686) (-1184 "VIEW3D.spad" 1905853 1905862 1921882 1921887) (-1183 "VIEW2D.spad" 1893752 1893761 1905843 1905848) (-1182 "VIEW.spad" 1891472 1891481 1893742 1893747) (-1181 "VECTOR2.spad" 1890111 1890124 1891462 1891467) (-1180 "VECTOR.spad" 1888830 1888841 1889081 1889108) (-1179 "VECTCAT.spad" 1886742 1886753 1888798 1888825) (-1178 "VECTCAT.spad" 1884463 1884476 1886521 1886526) (-1177 "VARIABLE.spad" 1884243 1884258 1884453 1884458) (-1176 "UTYPE.spad" 1883887 1883896 1884233 1884238) (-1175 "UTSODETL.spad" 1883182 1883206 1883843 1883848) (-1174 "UTSODE.spad" 1881398 1881418 1883172 1883177) (-1173 "UTSCAT.spad" 1878877 1878893 1881296 1881393) (-1172 "UTSCAT.spad" 1876024 1876042 1878445 1878450) (-1171 "UTS2.spad" 1875619 1875654 1876014 1876019) (-1170 "UTS.spad" 1870631 1870659 1874151 1874248) (-1169 "URAGG.spad" 1865352 1865363 1870621 1870626) (-1168 "URAGG.spad" 1860037 1860050 1865308 1865313) (-1167 "UPXSSING.spad" 1857805 1857831 1859241 1859374) (-1166 "UPXSCONS.spad" 1855623 1855643 1855996 1856145) (-1165 "UPXSCCA.spad" 1854194 1854214 1855469 1855618) (-1164 "UPXSCCA.spad" 1852907 1852929 1854184 1854189) (-1163 "UPXSCAT.spad" 1851496 1851512 1852753 1852902) (-1162 "UPXS2.spad" 1851039 1851092 1851486 1851491) (-1161 "UPXS.spad" 1848394 1848422 1849230 1849379) (-1160 "UPSQFREE.spad" 1846809 1846823 1848384 1848389) (-1159 "UPSCAT.spad" 1844604 1844628 1846707 1846804) (-1158 "UPSCAT.spad" 1842100 1842126 1844205 1844210) (-1157 "UPOLYC2.spad" 1841571 1841590 1842090 1842095) (-1156 "UPOLYC.spad" 1836651 1836662 1841413 1841566) (-1155 "UPOLYC.spad" 1831649 1831662 1836413 1836418) (-1154 "UPMP.spad" 1830581 1830594 1831639 1831644) (-1153 "UPDIVP.spad" 1830146 1830160 1830571 1830576) (-1152 "UPDECOMP.spad" 1828407 1828421 1830136 1830141) (-1151 "UPCDEN.spad" 1827624 1827640 1828397 1828402) (-1150 "UP2.spad" 1826988 1827009 1827614 1827619) (-1149 "UP.spad" 1824458 1824473 1824845 1824998) (-1148 "UNISEG2.spad" 1823955 1823968 1824414 1824419) (-1147 "UNISEG.spad" 1823308 1823319 1823874 1823879) (-1146 "UNIFACT.spad" 1822411 1822423 1823298 1823303) (-1145 "ULSCONS.spad" 1816257 1816277 1816627 1816776) (-1144 "ULSCCAT.spad" 1813994 1814014 1816103 1816252) (-1143 "ULSCCAT.spad" 1811839 1811861 1813950 1813955) (-1142 "ULSCAT.spad" 1810079 1810095 1811685 1811834) (-1141 "ULS2.spad" 1809593 1809646 1810069 1810074) (-1140 "ULS.spad" 1801626 1801654 1802571 1802994) (-1139 "UINT8.spad" 1801503 1801512 1801616 1801621) (-1138 "UINT64.spad" 1801379 1801388 1801493 1801498) (-1137 "UINT32.spad" 1801255 1801264 1801369 1801374) (-1136 "UINT16.spad" 1801131 1801140 1801245 1801250) (-1135 "UFD.spad" 1800196 1800205 1801057 1801126) (-1134 "UFD.spad" 1799323 1799334 1800186 1800191) (-1133 "UDVO.spad" 1798204 1798213 1799313 1799318) (-1132 "UDPO.spad" 1795785 1795796 1798160 1798165) (-1131 "TYPEAST.spad" 1795704 1795713 1795775 1795780) (-1130 "TYPE.spad" 1795636 1795645 1795694 1795699) (-1129 "TWOFACT.spad" 1794288 1794303 1795626 1795631) (-1128 "TUPLE.spad" 1793795 1793806 1794200 1794205) (-1127 "TUBETOOL.spad" 1790662 1790671 1793785 1793790) (-1126 "TUBE.spad" 1789309 1789326 1790652 1790657) (-1125 "TSETCAT.spad" 1777380 1777397 1789277 1789304) (-1124 "TSETCAT.spad" 1765437 1765456 1777336 1777341) (-1123 "TS.spad" 1764065 1764081 1765031 1765128) (-1122 "TRMANIP.spad" 1758429 1758446 1763753 1763758) (-1121 "TRIMAT.spad" 1757392 1757417 1758419 1758424) (-1120 "TRIGMNIP.spad" 1755919 1755936 1757382 1757387) (-1119 "TRIGCAT.spad" 1755431 1755440 1755909 1755914) (-1118 "TRIGCAT.spad" 1754941 1754952 1755421 1755426) (-1117 "TREE.spad" 1753581 1753592 1754613 1754640) (-1116 "TRANFUN.spad" 1753420 1753429 1753571 1753576) (-1115 "TRANFUN.spad" 1753257 1753268 1753410 1753415) (-1114 "TOPSP.spad" 1752931 1752940 1753247 1753252) (-1113 "TOOLSIGN.spad" 1752594 1752605 1752921 1752926) (-1112 "TEXTFILE.spad" 1751155 1751164 1752584 1752589) (-1111 "TEX1.spad" 1750711 1750722 1751145 1751150) (-1110 "TEX.spad" 1747905 1747914 1750701 1750706) (-1109 "TBCMPPK.spad" 1746006 1746029 1747895 1747900) (-1108 "TBAGG.spad" 1745249 1745272 1745974 1746001) (-1107 "TBAGG.spad" 1744512 1744537 1745239 1745244) (-1106 "TANEXP.spad" 1743920 1743931 1744502 1744507) (-1105 "TALGOP.spad" 1743644 1743655 1743910 1743915) (-1104 "TABLEAU.spad" 1743125 1743136 1743634 1743639) (-1103 "TABLE.spad" 1741400 1741423 1741670 1741697) (-1102 "TABLBUMP.spad" 1738179 1738190 1741390 1741395) (-1101 "SYSTEM.spad" 1737407 1737416 1738169 1738174) (-1100 "SYSSOLP.spad" 1734890 1734901 1737397 1737402) (-1099 "SYSPTR.spad" 1734789 1734798 1734880 1734885) (-1098 "SYSNNI.spad" 1734012 1734023 1734779 1734784) (-1097 "SYSINT.spad" 1733416 1733427 1734002 1734007) (-1096 "SYNTAX.spad" 1729750 1729759 1733406 1733411) (-1095 "SYMTAB.spad" 1727818 1727827 1729740 1729745) (-1094 "SYMS.spad" 1723847 1723856 1727808 1727813) (-1093 "SYMPOLY.spad" 1722980 1722991 1723062 1723189) (-1092 "SYMFUNC.spad" 1722481 1722492 1722970 1722975) (-1091 "SYMBOL.spad" 1719976 1719985 1722471 1722476) (-1090 "SUTS.spad" 1717089 1717117 1718508 1718605) (-1089 "SUPXS.spad" 1714431 1714459 1715280 1715429) (-1088 "SUPFRACF.spad" 1713536 1713554 1714421 1714426) (-1087 "SUP2.spad" 1712928 1712941 1713526 1713531) (-1086 "SUP.spad" 1710012 1710023 1710785 1710938) (-1085 "SUMRF.spad" 1708986 1708997 1710002 1710007) (-1084 "SUMFS.spad" 1708615 1708632 1708976 1708981) (-1083 "SULS.spad" 1700635 1700663 1701593 1702016) (-1082 "syntax.spad" 1700404 1700413 1700625 1700630) (-1081 "SUCH.spad" 1700094 1700109 1700394 1700399) (-1080 "SUBSPACE.spad" 1692225 1692240 1700084 1700089) (-1079 "SUBRESP.spad" 1691395 1691409 1692181 1692186) (-1078 "STTFNC.spad" 1687863 1687879 1691385 1691390) (-1077 "STTF.spad" 1683962 1683978 1687853 1687858) (-1076 "STTAYLOR.spad" 1676639 1676650 1683869 1683874) (-1075 "STRTBL.spad" 1675026 1675043 1675175 1675202) (-1074 "STRING.spad" 1673894 1673903 1674279 1674306) (-1073 "STREAM3.spad" 1673467 1673482 1673884 1673889) (-1072 "STREAM2.spad" 1672595 1672608 1673457 1673462) (-1071 "STREAM1.spad" 1672301 1672312 1672585 1672590) (-1070 "STREAM.spad" 1669297 1669308 1671904 1671919) (-1069 "STINPROD.spad" 1668233 1668249 1669287 1669292) (-1068 "STEPAST.spad" 1667467 1667476 1668223 1668228) (-1067 "STEP.spad" 1666784 1666793 1667457 1667462) (-1066 "STBL.spad" 1665162 1665190 1665329 1665356) (-1065 "STAGG.spad" 1663861 1663872 1665152 1665157) (-1064 "STAGG.spad" 1662558 1662571 1663851 1663856) (-1063 "STACK.spad" 1661980 1661991 1662230 1662257) (-1062 "SRING.spad" 1661740 1661749 1661970 1661975) (-1061 "SREGSET.spad" 1659472 1659489 1661374 1661401) (-1060 "SRDCMPK.spad" 1658049 1658069 1659462 1659467) (-1059 "SRAGG.spad" 1653232 1653241 1658017 1658044) (-1058 "SRAGG.spad" 1648435 1648446 1653222 1653227) (-1057 "SQMATRIX.spad" 1646112 1646130 1647028 1647115) (-1056 "SPLTREE.spad" 1640854 1640867 1645650 1645677) (-1055 "SPLNODE.spad" 1637474 1637487 1640844 1640849) (-1054 "SPFCAT.spad" 1636283 1636292 1637464 1637469) (-1053 "SPECOUT.spad" 1634835 1634844 1636273 1636278) (-1052 "SPADXPT.spad" 1626926 1626935 1634825 1634830) (-1051 "spad-parser.spad" 1626391 1626400 1626916 1626921) (-1050 "SPADAST.spad" 1626092 1626101 1626381 1626386) (-1049 "SPACEC.spad" 1610307 1610318 1626082 1626087) (-1048 "SPACE3.spad" 1610083 1610094 1610297 1610302) (-1047 "SORTPAK.spad" 1609632 1609645 1610039 1610044) (-1046 "SOLVETRA.spad" 1607395 1607406 1609622 1609627) (-1045 "SOLVESER.spad" 1605851 1605862 1607385 1607390) (-1044 "SOLVERAD.spad" 1601877 1601888 1605841 1605846) (-1043 "SOLVEFOR.spad" 1600339 1600357 1601867 1601872) (-1042 "SNTSCAT.spad" 1599939 1599956 1600307 1600334) (-1041 "SMTS.spad" 1598256 1598282 1599533 1599630) (-1040 "SMP.spad" 1596064 1596084 1596454 1596581) (-1039 "SMITH.spad" 1594909 1594934 1596054 1596059) (-1038 "SMATCAT.spad" 1593027 1593057 1594853 1594904) (-1037 "SMATCAT.spad" 1591077 1591109 1592905 1592910) (-1036 "aggcat.spad" 1590753 1590764 1591057 1591072) (-1035 "SKAGG.spad" 1589722 1589733 1590721 1590748) (-1034 "SINT.spad" 1589021 1589030 1589588 1589717) (-1033 "SIMPAN.spad" 1588749 1588758 1589011 1589016) (-1032 "SIGNRF.spad" 1587874 1587885 1588739 1588744) (-1031 "SIGNEF.spad" 1587160 1587177 1587864 1587869) (-1030 "syntax.spad" 1586577 1586586 1587150 1587155) (-1029 "SIG.spad" 1585939 1585948 1586567 1586572) (-1028 "SHP.spad" 1583883 1583898 1585895 1585900) (-1027 "SHDP.spad" 1573376 1573403 1573893 1573990) (-1026 "SGROUP.spad" 1572984 1572993 1573366 1573371) (-1025 "SGROUP.spad" 1572590 1572601 1572974 1572979) (-1024 "catdef.spad" 1572300 1572312 1572411 1572585) (-1023 "catdef.spad" 1571856 1571868 1572121 1572295) (-1022 "SGCF.spad" 1564995 1565004 1571846 1571851) (-1021 "SFRTCAT.spad" 1563941 1563958 1564963 1564990) (-1020 "SFRGCD.spad" 1563004 1563024 1563931 1563936) (-1019 "SFQCMPK.spad" 1557817 1557837 1562994 1562999) (-1018 "SEXOF.spad" 1557660 1557700 1557807 1557812) (-1017 "SEXCAT.spad" 1555488 1555528 1557650 1557655) (-1016 "SEX.spad" 1555380 1555389 1555478 1555483) (-1015 "SETMN.spad" 1553840 1553857 1555370 1555375) (-1014 "SETCAT.spad" 1553325 1553334 1553830 1553835) (-1013 "SETCAT.spad" 1552808 1552819 1553315 1553320) (-1012 "SETAGG.spad" 1549357 1549368 1552788 1552803) (-1011 "SETAGG.spad" 1545914 1545927 1549347 1549352) (-1010 "SET.spad" 1544223 1544234 1545320 1545359) (-1009 "syntax.spad" 1543926 1543935 1544213 1544218) (-1008 "SEGXCAT.spad" 1543082 1543095 1543916 1543921) (-1007 "SEGCAT.spad" 1542007 1542018 1543072 1543077) (-1006 "SEGBIND2.spad" 1541705 1541718 1541997 1542002) (-1005 "SEGBIND.spad" 1541463 1541474 1541652 1541657) (-1004 "SEGAST.spad" 1541193 1541202 1541453 1541458) (-1003 "SEG2.spad" 1540628 1540641 1541149 1541154) (-1002 "SEG.spad" 1540441 1540452 1540547 1540552) (-1001 "SDVAR.spad" 1539717 1539728 1540431 1540436) (-1000 "SDPOL.spad" 1537409 1537420 1537700 1537827) (-999 "SCPKG.spad" 1535499 1535509 1537399 1537404) (-998 "SCOPE.spad" 1534677 1534685 1535489 1535494) (-997 "SCACHE.spad" 1533374 1533384 1534667 1534672) (-996 "SASTCAT.spad" 1533284 1533292 1533364 1533369) (-995 "SAOS.spad" 1533157 1533165 1533274 1533279) (-994 "SAERFFC.spad" 1532871 1532890 1533147 1533152) (-993 "SAEFACT.spad" 1532573 1532592 1532861 1532866) (-992 "SAE.spad" 1530224 1530239 1530834 1530969) (-991 "RURPK.spad" 1527884 1527899 1530214 1530219) (-990 "RULESET.spad" 1527338 1527361 1527874 1527879) (-989 "RULECOLD.spad" 1527191 1527203 1527328 1527333) (-988 "RULE.spad" 1525440 1525463 1527181 1527186) (-987 "RTVALUE.spad" 1525176 1525184 1525430 1525435) (-986 "syntax.spad" 1524894 1524902 1525166 1525171) (-985 "RSETGCD.spad" 1521337 1521356 1524884 1524889) (-984 "RSETCAT.spad" 1511306 1511322 1521305 1521332) (-983 "RSETCAT.spad" 1501295 1501313 1511296 1511301) (-982 "RSDCMPK.spad" 1499796 1499815 1501285 1501290) (-981 "RRCC.spad" 1498181 1498210 1499786 1499791) (-980 "RRCC.spad" 1496564 1496595 1498171 1498176) (-979 "RPTAST.spad" 1496267 1496275 1496554 1496559) (-978 "RPOLCAT.spad" 1475772 1475786 1496135 1496262) (-977 "RPOLCAT.spad" 1455070 1455086 1475435 1475440) (-976 "ROMAN.spad" 1454399 1454407 1454936 1455065) (-975 "ROIRC.spad" 1453480 1453511 1454389 1454394) (-974 "RNS.spad" 1452457 1452465 1453382 1453475) (-973 "RNS.spad" 1451520 1451530 1452447 1452452) (-972 "RNGBIND.spad" 1450681 1450694 1451475 1451480) (-971 "RNG.spad" 1450290 1450298 1450671 1450676) (-970 "RNG.spad" 1449897 1449907 1450280 1450285) (-969 "RMODULE.spad" 1449679 1449689 1449887 1449892) (-968 "RMCAT2.spad" 1449100 1449156 1449669 1449674) (-967 "RMATRIX.spad" 1447910 1447928 1448252 1448291) (-966 "RMATCAT.spad" 1443548 1443578 1447866 1447905) (-965 "RMATCAT.spad" 1439076 1439108 1443396 1443401) (-964 "RLINSET.spad" 1438781 1438791 1439066 1439071) (-963 "RINTERP.spad" 1438670 1438689 1438771 1438776) (-962 "RING.spad" 1438141 1438149 1438650 1438665) (-961 "RING.spad" 1437620 1437630 1438131 1438136) (-960 "RIDIST.spad" 1437013 1437021 1437610 1437615) (-959 "RGCHAIN.spad" 1435568 1435583 1436461 1436488) (-958 "RGBCSPC.spad" 1435358 1435369 1435558 1435563) (-957 "RGBCMDL.spad" 1434921 1434932 1435348 1435353) (-956 "RFFACTOR.spad" 1434384 1434394 1434911 1434916) (-955 "RFFACT.spad" 1434120 1434131 1434374 1434379) (-954 "RFDIST.spad" 1433117 1433125 1434110 1434115) (-953 "RF.spad" 1430792 1430802 1433107 1433112) (-952 "RETSOL.spad" 1430212 1430224 1430782 1430787) (-951 "RETRACT.spad" 1429641 1429651 1430202 1430207) (-950 "RETRACT.spad" 1429068 1429080 1429631 1429636) (-949 "RETAST.spad" 1428881 1428889 1429058 1429063) (-948 "RESRING.spad" 1428229 1428275 1428819 1428876) (-947 "RESLATC.spad" 1427554 1427564 1428219 1428224) (-946 "REPSQ.spad" 1427286 1427296 1427544 1427549) (-945 "REPDB.spad" 1426994 1427004 1427276 1427281) (-944 "REP2.spad" 1416709 1416719 1426836 1426841) (-943 "REP1.spad" 1410930 1410940 1416659 1416664) (-942 "REP.spad" 1408485 1408493 1410920 1410925) (-941 "REGSET.spad" 1406311 1406327 1408119 1408146) (-940 "REF.spad" 1405830 1405840 1406301 1406306) (-939 "REDORDER.spad" 1405037 1405053 1405820 1405825) (-938 "RECLOS.spad" 1403934 1403953 1404637 1404730) (-937 "REALSOLV.spad" 1403075 1403083 1403924 1403929) (-936 "REAL0Q.spad" 1400374 1400388 1403065 1403070) (-935 "REAL0.spad" 1397219 1397233 1400364 1400369) (-934 "REAL.spad" 1397092 1397100 1397209 1397214) (-933 "RDUCEAST.spad" 1396814 1396822 1397082 1397087) (-932 "RDIV.spad" 1396470 1396494 1396804 1396809) (-931 "RDIST.spad" 1396038 1396048 1396460 1396465) (-930 "RDETRS.spad" 1394903 1394920 1396028 1396033) (-929 "RDETR.spad" 1393043 1393060 1394893 1394898) (-928 "RDEEFS.spad" 1392143 1392159 1393033 1393038) (-927 "RDEEF.spad" 1391154 1391170 1392133 1392138) (-926 "RCFIELD.spad" 1388373 1388381 1391056 1391149) (-925 "RCFIELD.spad" 1385678 1385688 1388363 1388368) (-924 "RCAGG.spad" 1383615 1383625 1385668 1385673) (-923 "RCAGG.spad" 1381479 1381491 1383534 1383539) (-922 "RATRET.spad" 1380840 1380850 1381469 1381474) (-921 "RATFACT.spad" 1380533 1380544 1380830 1380835) (-920 "RANDSRC.spad" 1379853 1379861 1380523 1380528) (-919 "RADUTIL.spad" 1379610 1379618 1379843 1379848) (-918 "RADIX.spad" 1376655 1376668 1378200 1378293) (-917 "RADFF.spad" 1374572 1374608 1374690 1374846) (-916 "RADCAT.spad" 1374168 1374176 1374562 1374567) (-915 "RADCAT.spad" 1373762 1373772 1374158 1374163) (-914 "QUEUE.spad" 1373176 1373186 1373434 1373461) (-913 "QUATCT2.spad" 1372797 1372815 1373166 1373171) (-912 "QUATCAT.spad" 1370968 1370978 1372727 1372792) (-911 "QUATCAT.spad" 1368904 1368916 1370665 1370670) (-910 "QUAT.spad" 1367511 1367521 1367853 1367918) (-909 "QUAGG.spad" 1366345 1366355 1367479 1367506) (-908 "QQUTAST.spad" 1366114 1366122 1366335 1366340) (-907 "QFORM.spad" 1365733 1365747 1366104 1366109) (-906 "QFCAT2.spad" 1365426 1365442 1365723 1365728) (-905 "QFCAT.spad" 1364129 1364139 1365328 1365421) (-904 "QFCAT.spad" 1362465 1362477 1363666 1363671) (-903 "QEQUAT.spad" 1362024 1362032 1362455 1362460) (-902 "QCMPACK.spad" 1356939 1356958 1362014 1362019) (-901 "QALGSET2.spad" 1354935 1354953 1356929 1356934) (-900 "QALGSET.spad" 1351040 1351072 1354849 1354854) (-899 "PWFFINTB.spad" 1348456 1348477 1351030 1351035) (-898 "PUSHVAR.spad" 1347795 1347814 1348446 1348451) (-897 "PTRANFN.spad" 1343931 1343941 1347785 1347790) (-896 "PTPACK.spad" 1341019 1341029 1343921 1343926) (-895 "PTFUNC2.spad" 1340842 1340856 1341009 1341014) (-894 "PTCAT.spad" 1340097 1340107 1340810 1340837) (-893 "PSQFR.spad" 1339412 1339436 1340087 1340092) (-892 "PSEUDLIN.spad" 1338298 1338308 1339402 1339407) (-891 "PSETPK.spad" 1325003 1325019 1338176 1338181) (-890 "PSETCAT.spad" 1319403 1319426 1324983 1324998) (-889 "PSETCAT.spad" 1313777 1313802 1319359 1319364) (-888 "PSCURVE.spad" 1312776 1312784 1313767 1313772) (-887 "PSCAT.spad" 1311559 1311588 1312674 1312771) (-886 "PSCAT.spad" 1310432 1310463 1311549 1311554) (-885 "PRTITION.spad" 1309130 1309138 1310422 1310427) (-884 "PRTDAST.spad" 1308849 1308857 1309120 1309125) (-883 "PRS.spad" 1298467 1298484 1308805 1308810) (-882 "PRQAGG.spad" 1297902 1297912 1298435 1298462) (-881 "PROPLOG.spad" 1297506 1297514 1297892 1297897) (-880 "PROPFUN2.spad" 1297129 1297142 1297496 1297501) (-879 "PROPFUN1.spad" 1296535 1296546 1297119 1297124) (-878 "PROPFRML.spad" 1295103 1295114 1296525 1296530) (-877 "PROPERTY.spad" 1294599 1294607 1295093 1295098) (-876 "PRODUCT.spad" 1292296 1292308 1292580 1292635) (-875 "PRINT.spad" 1292048 1292056 1292286 1292291) (-874 "PRIMES.spad" 1290309 1290319 1292038 1292043) (-873 "PRIMELT.spad" 1288430 1288444 1290299 1290304) (-872 "PRIMCAT.spad" 1288073 1288081 1288420 1288425) (-871 "PRIMARR2.spad" 1286840 1286852 1288063 1288068) (-870 "PRIMARR.spad" 1285895 1285905 1286065 1286092) (-869 "PREASSOC.spad" 1285277 1285289 1285885 1285890) (-868 "PR.spad" 1283795 1283807 1284494 1284621) (-867 "PPCURVE.spad" 1282932 1282940 1283785 1283790) (-866 "PORTNUM.spad" 1282723 1282731 1282922 1282927) (-865 "POLYROOT.spad" 1281572 1281594 1282679 1282684) (-864 "POLYLIFT.spad" 1280837 1280860 1281562 1281567) (-863 "POLYCATQ.spad" 1278963 1278985 1280827 1280832) (-862 "POLYCAT.spad" 1272465 1272486 1278831 1278958) (-861 "POLYCAT.spad" 1265487 1265510 1271855 1271860) (-860 "POLY2UP.spad" 1264939 1264953 1265477 1265482) (-859 "POLY2.spad" 1264536 1264548 1264929 1264934) (-858 "POLY.spad" 1262204 1262214 1262719 1262846) (-857 "POLUTIL.spad" 1261169 1261198 1262160 1262165) (-856 "POLTOPOL.spad" 1259917 1259932 1261159 1261164) (-855 "POINT.spad" 1258800 1258810 1258887 1258914) (-854 "PNTHEORY.spad" 1255502 1255510 1258790 1258795) (-853 "PMTOOLS.spad" 1254277 1254291 1255492 1255497) (-852 "PMSYM.spad" 1253826 1253836 1254267 1254272) (-851 "PMQFCAT.spad" 1253417 1253431 1253816 1253821) (-850 "PMPREDFS.spad" 1252879 1252901 1253407 1253412) (-849 "PMPRED.spad" 1252366 1252380 1252869 1252874) (-848 "PMPLCAT.spad" 1251443 1251461 1252295 1252300) (-847 "PMLSAGG.spad" 1251028 1251042 1251433 1251438) (-846 "PMKERNEL.spad" 1250607 1250619 1251018 1251023) (-845 "PMINS.spad" 1250187 1250197 1250597 1250602) (-844 "PMFS.spad" 1249764 1249782 1250177 1250182) (-843 "PMDOWN.spad" 1249054 1249068 1249754 1249759) (-842 "PMASSFS.spad" 1248029 1248045 1249044 1249049) (-841 "PMASS.spad" 1247047 1247055 1248019 1248024) (-840 "PLOTTOOL.spad" 1246827 1246835 1247037 1247042) (-839 "PLOT3D.spad" 1243291 1243299 1246817 1246822) (-838 "PLOT1.spad" 1242464 1242474 1243281 1243286) (-837 "PLOT.spad" 1237387 1237395 1242454 1242459) (-836 "PLEQN.spad" 1224789 1224816 1237377 1237382) (-835 "PINTERPA.spad" 1224573 1224589 1224779 1224784) (-834 "PINTERP.spad" 1224195 1224214 1224563 1224568) (-833 "PID.spad" 1223169 1223177 1224121 1224190) (-832 "PICOERCE.spad" 1222826 1222836 1223159 1223164) (-831 "PI.spad" 1222443 1222451 1222800 1222821) (-830 "PGROEB.spad" 1221052 1221066 1222433 1222438) (-829 "PGE.spad" 1212725 1212733 1221042 1221047) (-828 "PGCD.spad" 1211679 1211696 1212715 1212720) (-827 "PFRPAC.spad" 1210828 1210838 1211669 1211674) (-826 "PFR.spad" 1207531 1207541 1210730 1210823) (-825 "PFOTOOLS.spad" 1206789 1206805 1207521 1207526) (-824 "PFOQ.spad" 1206159 1206177 1206779 1206784) (-823 "PFO.spad" 1205578 1205605 1206149 1206154) (-822 "PFECAT.spad" 1203288 1203296 1205504 1205573) (-821 "PFECAT.spad" 1201026 1201036 1203244 1203249) (-820 "PFBRU.spad" 1198914 1198926 1201016 1201021) (-819 "PFBR.spad" 1196474 1196497 1198904 1198909) (-818 "PF.spad" 1196048 1196060 1196279 1196372) (-817 "PERMGRP.spad" 1190818 1190828 1196038 1196043) (-816 "PERMCAT.spad" 1189479 1189489 1190798 1190813) (-815 "PERMAN.spad" 1188035 1188049 1189469 1189474) (-814 "PERM.spad" 1183845 1183855 1187868 1187883) (-813 "PENDTREE.spad" 1183259 1183269 1183539 1183544) (-812 "PDSPC.spad" 1182072 1182082 1183249 1183254) (-811 "PDSPC.spad" 1180883 1180895 1182062 1182067) (-810 "PDRING.spad" 1180725 1180735 1180863 1180878) (-809 "PDMOD.spad" 1180541 1180553 1180693 1180720) (-808 "PDECOMP.spad" 1180011 1180028 1180531 1180536) (-807 "PDDOM.spad" 1179449 1179462 1180001 1180006) (-806 "PDDOM.spad" 1178885 1178900 1179439 1179444) (-805 "PCOMP.spad" 1178738 1178751 1178875 1178880) (-804 "PBWLB.spad" 1177336 1177353 1178728 1178733) (-803 "PATTERN2.spad" 1177074 1177086 1177326 1177331) (-802 "PATTERN1.spad" 1175418 1175434 1177064 1177069) (-801 "PATTERN.spad" 1169993 1170003 1175408 1175413) (-800 "PATRES2.spad" 1169665 1169679 1169983 1169988) (-799 "PATRES.spad" 1167248 1167260 1169655 1169660) (-798 "PATMATCH.spad" 1165489 1165520 1167000 1167005) (-797 "PATMAB.spad" 1164918 1164928 1165479 1165484) (-796 "PATLRES.spad" 1164004 1164018 1164908 1164913) (-795 "PATAB.spad" 1163768 1163778 1163994 1163999) (-794 "PARTPERM.spad" 1161824 1161832 1163758 1163763) (-793 "PARSURF.spad" 1161258 1161286 1161814 1161819) (-792 "PARSU2.spad" 1161055 1161071 1161248 1161253) (-791 "script-parser.spad" 1160575 1160583 1161045 1161050) (-790 "PARSCURV.spad" 1160009 1160037 1160565 1160570) (-789 "PARSC2.spad" 1159800 1159816 1159999 1160004) (-788 "PARPCURV.spad" 1159262 1159290 1159790 1159795) (-787 "PARPC2.spad" 1159053 1159069 1159252 1159257) (-786 "PARAMAST.spad" 1158181 1158189 1159043 1159048) (-785 "PAN2EXPR.spad" 1157593 1157601 1158171 1158176) (-784 "PALETTE.spad" 1156707 1156715 1157583 1157588) (-783 "PAIR.spad" 1155781 1155794 1156350 1156355) (-782 "PADICRC.spad" 1153186 1153204 1154349 1154442) (-781 "PADICRAT.spad" 1151246 1151258 1151459 1151552) (-780 "PADICCT.spad" 1149795 1149807 1151172 1151241) (-779 "PADIC.spad" 1149498 1149510 1149721 1149790) (-778 "PADEPAC.spad" 1148187 1148206 1149488 1149493) (-777 "PADE.spad" 1146939 1146955 1148177 1148182) (-776 "OWP.spad" 1146187 1146217 1146797 1146864) (-775 "OVERSET.spad" 1145760 1145768 1146177 1146182) (-774 "OVAR.spad" 1145541 1145564 1145750 1145755) (-773 "OUTFORM.spad" 1134949 1134957 1145531 1145536) (-772 "OUTBFILE.spad" 1134383 1134391 1134939 1134944) (-771 "OUTBCON.spad" 1133453 1133461 1134373 1134378) (-770 "OUTBCON.spad" 1132521 1132531 1133443 1133448) (-769 "OUT.spad" 1131639 1131647 1132511 1132516) (-768 "OSI.spad" 1131114 1131122 1131629 1131634) (-767 "OSGROUP.spad" 1131032 1131040 1131104 1131109) (-766 "ORTHPOL.spad" 1129543 1129553 1130975 1130980) (-765 "OREUP.spad" 1129037 1129065 1129264 1129303) (-764 "ORESUP.spad" 1128379 1128403 1128758 1128797) (-763 "OREPCTO.spad" 1126268 1126280 1128299 1128304) (-762 "OREPCAT.spad" 1120455 1120465 1126224 1126263) (-761 "OREPCAT.spad" 1114532 1114544 1120303 1120308) (-760 "ORDTYPE.spad" 1113769 1113777 1114522 1114527) (-759 "ORDTYPE.spad" 1113004 1113014 1113759 1113764) (-758 "ORDSTRCT.spad" 1112790 1112805 1112953 1112958) (-757 "ORDSET.spad" 1112490 1112498 1112780 1112785) (-756 "ORDRING.spad" 1112307 1112315 1112470 1112485) (-755 "ORDMON.spad" 1112162 1112170 1112297 1112302) (-754 "ORDFUNS.spad" 1111294 1111310 1112152 1112157) (-753 "ORDFIN.spad" 1111114 1111122 1111284 1111289) (-752 "ORDCOMP2.spad" 1110407 1110419 1111104 1111109) (-751 "ORDCOMP.spad" 1108933 1108943 1110015 1110044) (-750 "OPSIG.spad" 1108595 1108603 1108923 1108928) (-749 "OPQUERY.spad" 1108176 1108184 1108585 1108590) (-748 "OPERCAT.spad" 1107642 1107652 1108166 1108171) (-747 "OPERCAT.spad" 1107106 1107118 1107632 1107637) (-746 "OP.spad" 1106848 1106858 1106928 1106995) (-745 "ONECOMP2.spad" 1106272 1106284 1106838 1106843) (-744 "ONECOMP.spad" 1105078 1105088 1105880 1105909) (-743 "OMSAGG.spad" 1104866 1104876 1105034 1105073) (-742 "OMLO.spad" 1104299 1104311 1104752 1104791) (-741 "OINTDOM.spad" 1104062 1104070 1104225 1104294) (-740 "OFMONOID.spad" 1102201 1102211 1104018 1104023) (-739 "ODVAR.spad" 1101462 1101472 1102191 1102196) (-738 "ODR.spad" 1101106 1101132 1101274 1101423) (-737 "ODPOL.spad" 1098754 1098764 1099094 1099221) (-736 "ODP.spad" 1088391 1088411 1088764 1088861) (-735 "ODETOOLS.spad" 1087040 1087059 1088381 1088386) (-734 "ODESYS.spad" 1084734 1084751 1087030 1087035) (-733 "ODERTRIC.spad" 1080767 1080784 1084691 1084696) (-732 "ODERED.spad" 1080166 1080190 1080757 1080762) (-731 "ODERAT.spad" 1077799 1077816 1080156 1080161) (-730 "ODEPRRIC.spad" 1074892 1074914 1077789 1077794) (-729 "ODEPRIM.spad" 1072290 1072312 1074882 1074887) (-728 "ODEPAL.spad" 1071676 1071700 1072280 1072285) (-727 "ODEINT.spad" 1071111 1071127 1071666 1071671) (-726 "ODEEF.spad" 1066606 1066622 1071101 1071106) (-725 "ODECONST.spad" 1066151 1066169 1066596 1066601) (-724 "OCTCT2.spad" 1065792 1065810 1066141 1066146) (-723 "OCT.spad" 1064107 1064117 1064821 1064860) (-722 "OCAMON.spad" 1063955 1063963 1064097 1064102) (-721 "OC.spad" 1061751 1061761 1063911 1063950) (-720 "OC.spad" 1059286 1059298 1061448 1061453) (-719 "OASGP.spad" 1059101 1059109 1059276 1059281) (-718 "OAMONS.spad" 1058623 1058631 1059091 1059096) (-717 "OAMON.spad" 1058381 1058389 1058613 1058618) (-716 "OAMON.spad" 1058137 1058147 1058371 1058376) (-715 "OAGROUP.spad" 1057675 1057683 1058127 1058132) (-714 "OAGROUP.spad" 1057211 1057221 1057665 1057670) (-713 "NUMTUBE.spad" 1056802 1056818 1057201 1057206) (-712 "NUMQUAD.spad" 1044778 1044786 1056792 1056797) (-711 "NUMODE.spad" 1036130 1036138 1044768 1044773) (-710 "NUMFMT.spad" 1034970 1034978 1036120 1036125) (-709 "NUMERIC.spad" 1027085 1027095 1034776 1034781) (-708 "NTSCAT.spad" 1025593 1025609 1027053 1027080) (-707 "NTPOLFN.spad" 1025170 1025180 1025536 1025541) (-706 "NSUP2.spad" 1024562 1024574 1025160 1025165) (-705 "NSUP.spad" 1017999 1018009 1022419 1022572) (-704 "NSMP.spad" 1014911 1014930 1015203 1015330) (-703 "NREP.spad" 1013313 1013327 1014901 1014906) (-702 "NPCOEF.spad" 1012559 1012579 1013303 1013308) (-701 "NORMRETR.spad" 1012157 1012196 1012549 1012554) (-700 "NORMPK.spad" 1010099 1010118 1012147 1012152) (-699 "NORMMA.spad" 1009787 1009813 1010089 1010094) (-698 "NONE1.spad" 1009463 1009473 1009777 1009782) (-697 "NONE.spad" 1009204 1009212 1009453 1009458) (-696 "NODE1.spad" 1008691 1008707 1009194 1009199) (-695 "NNI.spad" 1007586 1007594 1008665 1008686) (-694 "NLINSOL.spad" 1006212 1006222 1007576 1007581) (-693 "NFINTBAS.spad" 1003772 1003789 1006202 1006207) (-692 "NETCLT.spad" 1003746 1003757 1003762 1003767) (-691 "NCODIV.spad" 1001970 1001986 1003736 1003741) (-690 "NCNTFRAC.spad" 1001612 1001626 1001960 1001965) (-689 "NCEP.spad" 999778 999792 1001602 1001607) (-688 "NASRING.spad" 999382 999390 999768 999773) (-687 "NASRING.spad" 998984 998994 999372 999377) (-686 "NARNG.spad" 998384 998392 998974 998979) (-685 "NARNG.spad" 997782 997792 998374 998379) (-684 "NAALG.spad" 997347 997357 997750 997777) (-683 "NAALG.spad" 996932 996944 997337 997342) (-682 "MULTSQFR.spad" 993890 993907 996922 996927) (-681 "MULTFACT.spad" 993273 993290 993880 993885) (-680 "MTSCAT.spad" 991367 991388 993171 993268) (-679 "MTHING.spad" 991026 991036 991357 991362) (-678 "MSYSCMD.spad" 990460 990468 991016 991021) (-677 "MSETAGG.spad" 990305 990315 990428 990455) (-676 "MSET.spad" 988254 988264 989999 990038) (-675 "MRING.spad" 985231 985243 987962 988029) (-674 "MRF2.spad" 984793 984807 985221 985226) (-673 "MRATFAC.spad" 984339 984356 984783 984788) (-672 "MPRFF.spad" 982379 982398 984329 984334) (-671 "MPOLY.spad" 980183 980198 980542 980669) (-670 "MPCPF.spad" 979447 979466 980173 980178) (-669 "MPC3.spad" 979264 979304 979437 979442) (-668 "MPC2.spad" 978918 978951 979254 979259) (-667 "MONOTOOL.spad" 977269 977286 978908 978913) (-666 "catdef.spad" 976702 976713 976923 977264) (-665 "catdef.spad" 976100 976111 976356 976697) (-664 "MONOID.spad" 975421 975429 976090 976095) (-663 "MONOID.spad" 974740 974750 975411 975416) (-662 "MONOGEN.spad" 973488 973501 974600 974735) (-661 "MONOGEN.spad" 972258 972273 973372 973377) (-660 "MONADWU.spad" 970338 970346 972248 972253) (-659 "MONADWU.spad" 968416 968426 970328 970333) (-658 "MONAD.spad" 967576 967584 968406 968411) (-657 "MONAD.spad" 966734 966744 967566 967571) (-656 "MOEBIUS.spad" 965470 965484 966714 966729) (-655 "MODULE.spad" 965340 965350 965438 965465) (-654 "MODULE.spad" 965230 965242 965330 965335) (-653 "MODRING.spad" 964565 964604 965210 965225) (-652 "MODOP.spad" 963222 963234 964387 964454) (-651 "MODMONOM.spad" 962953 962971 963212 963217) (-650 "MODMON.spad" 960023 960035 960738 960891) (-649 "MODFIELD.spad" 959385 959424 959925 960018) (-648 "MMLFORM.spad" 958245 958253 959375 959380) (-647 "MMAP.spad" 957987 958021 958235 958240) (-646 "MLO.spad" 956446 956456 957943 957982) (-645 "MLIFT.spad" 955058 955075 956436 956441) (-644 "MKUCFUNC.spad" 954593 954611 955048 955053) (-643 "MKRECORD.spad" 954181 954194 954583 954588) (-642 "MKFUNC.spad" 953588 953598 954171 954176) (-641 "MKFLCFN.spad" 952556 952566 953578 953583) (-640 "MKBCFUNC.spad" 952051 952069 952546 952551) (-639 "MHROWRED.spad" 950562 950572 952041 952046) (-638 "MFINFACT.spad" 949962 949984 950552 950557) (-637 "MESH.spad" 947757 947765 949952 949957) (-636 "MDDFACT.spad" 945976 945986 947747 947752) (-635 "MDAGG.spad" 945267 945277 945956 945971) (-634 "MCDEN.spad" 944477 944489 945257 945262) (-633 "MAYBE.spad" 943777 943788 944467 944472) (-632 "MATSTOR.spad" 941093 941103 943767 943772) (-631 "MATRIX.spad" 939872 939882 940356 940383) (-630 "MATLIN.spad" 937240 937264 939756 939761) (-629 "MATCAT2.spad" 936522 936570 937230 937235) (-628 "MATCAT.spad" 928218 928240 936490 936517) (-627 "MATCAT.spad" 919786 919810 928060 928065) (-626 "MAPPKG3.spad" 918701 918715 919776 919781) (-625 "MAPPKG2.spad" 918039 918051 918691 918696) (-624 "MAPPKG1.spad" 916867 916877 918029 918034) (-623 "MAPPAST.spad" 916206 916214 916857 916862) (-622 "MAPHACK3.spad" 916018 916032 916196 916201) (-621 "MAPHACK2.spad" 915787 915799 916008 916013) (-620 "MAPHACK1.spad" 915431 915441 915777 915782) (-619 "MAGMA.spad" 913237 913254 915421 915426) (-618 "MACROAST.spad" 912832 912840 913227 913232) (-617 "LZSTAGG.spad" 910086 910096 912822 912827) (-616 "LZSTAGG.spad" 907338 907350 910076 910081) (-615 "LWORD.spad" 904083 904100 907328 907333) (-614 "LSTAST.spad" 903867 903875 904073 904078) (-613 "LSQM.spad" 902145 902159 902539 902590) (-612 "LSPP.spad" 901680 901697 902135 902140) (-611 "LSMP1.spad" 899523 899537 901670 901675) (-610 "LSMP.spad" 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415134 415158 415666 415671) (-282 "FCTRDATA.spad" 414142 414150 415124 415129) (-281 "FCOMP.spad" 413521 413531 414132 414137) (-280 "FAXF.spad" 406556 406570 413423 413516) (-279 "FAXF.spad" 399643 399659 406512 406517) (-278 "FARRAY.spad" 397835 397845 398868 398895) (-277 "FAMR.spad" 395979 395991 397733 397830) (-276 "FAMR.spad" 394107 394121 395863 395868) (-275 "FAMONOID.spad" 393791 393801 394061 394066) (-274 "FAMONC.spad" 392111 392123 393781 393786) (-273 "FAGROUP.spad" 391751 391761 392007 392034) (-272 "FACUTIL.spad" 389963 389980 391741 391746) (-271 "FACTFUNC.spad" 389165 389175 389953 389958) (-270 "EXPUPXS.spad" 386057 386080 387356 387505) (-269 "EXPRTUBE.spad" 383345 383353 386047 386052) (-268 "EXPRODE.spad" 380513 380529 383335 383340) (-267 "EXPR2UPS.spad" 376635 376648 380503 380508) (-266 "EXPR2.spad" 376340 376352 376625 376630) (-265 "EXPR.spad" 371985 371995 372699 372986) (-264 "EXPEXPAN.spad" 368930 368955 369562 369655) (-263 "EXITAST.spad" 368666 368674 368920 368925) (-262 "EXIT.spad" 368337 368345 368656 368661) (-261 "EVALCYC.spad" 367797 367811 368327 368332) (-260 "EVALAB.spad" 367377 367387 367787 367792) (-259 "EVALAB.spad" 366955 366967 367367 367372) (-258 "EUCDOM.spad" 364545 364553 366881 366950) (-257 "EUCDOM.spad" 362197 362207 364535 364540) (-256 "ES2.spad" 361710 361726 362187 362192) (-255 "ES1.spad" 361280 361296 361700 361705) (-254 "ES.spad" 354151 354159 361270 361275) (-253 "ES.spad" 346943 346953 354064 354069) (-252 "ERROR.spad" 344270 344278 346933 346938) (-251 "EQTBL.spad" 342606 342628 342815 342842) (-250 "EQ2.spad" 342324 342336 342596 342601) (-249 "EQ.spad" 337230 337240 340025 340131) (-248 "EP.spad" 333556 333566 337220 337225) (-247 "ENV.spad" 332234 332242 333546 333551) (-246 "ENTIRER.spad" 331902 331910 332178 332229) (-245 "ENTIRER.spad" 331614 331624 331892 331897) (-244 "EMR.spad" 330902 330943 331540 331609) (-243 "ELTAGG.spad" 329156 329175 330892 330897) (-242 "ELTAGG.spad" 327374 327395 329112 329117) (-241 "ELTAB.spad" 326849 326862 327364 327369) (-240 "ELFUTS.spad" 326284 326303 326839 326844) (-239 "ELEMFUN.spad" 325973 325981 326274 326279) (-238 "ELEMFUN.spad" 325660 325670 325963 325968) (-237 "ELAGG.spad" 323631 323641 325640 325655) (-236 "ELAGG.spad" 321539 321551 323550 323555) (-235 "ELABOR.spad" 320885 320893 321529 321534) (-234 "ELABEXPR.spad" 319817 319825 320875 320880) (-233 "EFUPXS.spad" 316593 316623 319773 319778) (-232 "EFULS.spad" 313429 313452 316549 316554) (-231 "EFSTRUC.spad" 311444 311460 313419 313424) (-230 "EF.spad" 306220 306236 311434 311439) (-229 "EAB.spad" 304520 304528 306210 306215) (-228 "DVARCAT.spad" 301526 301536 304510 304515) (-227 "DVARCAT.spad" 298530 298542 301516 301521) (-226 "DSMP.spad" 296263 296277 296568 296695) (-225 "DSEXT.spad" 295565 295575 296253 296258) (-224 "DSEXT.spad" 294787 294799 295477 295482) (-223 "DROPT1.spad" 294452 294462 294777 294782) (-222 "DROPT0.spad" 289317 289325 294442 294447) (-221 "DROPT.spad" 283276 283284 289307 289312) (-220 "DRAWPT.spad" 281449 281457 283266 283271) (-219 "DRAWHACK.spad" 280757 280767 281439 281444) (-218 "DRAWCX.spad" 278235 278243 280747 280752) (-217 "DRAWCURV.spad" 277782 277797 278225 278230) (-216 "DRAWCFUN.spad" 267314 267322 277772 277777) (-215 "DRAW.spad" 260190 260203 267304 267309) (-214 "DQAGG.spad" 258368 258378 260158 260185) (-213 "DPOLCAT.spad" 253725 253741 258236 258363) (-212 "DPOLCAT.spad" 249168 249186 253681 253686) (-211 "DPMO.spad" 241871 241887 242009 242215) (-210 "DPMM.spad" 234587 234605 234712 234918) (-209 "DOMTMPLT.spad" 234358 234366 234577 234582) (-208 "DOMCTOR.spad" 234113 234121 234348 234353) (-207 "DOMAIN.spad" 233224 233232 234103 234108) (-206 "DMP.spad" 230817 230832 231387 231514) (-205 "DMEXT.spad" 230684 230694 230785 230812) (-204 "DLP.spad" 230044 230054 230674 230679) (-203 "DLIST.spad" 228665 228675 229269 229296) (-202 "DLAGG.spad" 227082 227092 228655 228660) (-201 "DIVRING.spad" 226624 226632 227026 227077) (-200 "DIVRING.spad" 226210 226220 226614 226619) (-199 "DISPLAY.spad" 224400 224408 226200 226205) (-198 "DIRPROD2.spad" 223218 223236 224390 224395) (-197 "DIRPROD.spad" 212588 212604 213228 213325) (-196 "DIRPCAT.spad" 211871 211887 212486 212583) (-195 "DIRPCAT.spad" 210780 210798 211397 211402) (-194 "DIOSP.spad" 209605 209613 210770 210775) (-193 "DIOPS.spad" 208601 208611 209585 209600) (-192 "DIOPS.spad" 207571 207583 208557 208562) (-191 "catdef.spad" 207429 207437 207561 207566) (-190 "DIFRING.spad" 207267 207275 207409 207424) (-189 "DIFFSPC.spad" 206846 206854 207257 207262) (-188 "DIFFSPC.spad" 206423 206433 206836 206841) (-187 "DIFFMOD.spad" 205912 205922 206391 206418) (-186 "DIFFDOM.spad" 205077 205088 205902 205907) (-185 "DIFFDOM.spad" 204240 204253 205067 205072) (-184 "DIFEXT.spad" 204059 204069 204220 204235) (-183 "DIAGG.spad" 203689 203699 204039 204054) (-182 "DIAGG.spad" 203327 203339 203679 203684) (-181 "DHMATRIX.spad" 201704 201714 202849 202876) (-180 "DFSFUN.spad" 195344 195352 201694 201699) (-179 "DFLOAT.spad" 191951 191959 195234 195339) (-178 "DFINTTLS.spad" 190182 190198 191941 191946) (-177 "DERHAM.spad" 188096 188128 190162 190177) (-176 "DEQUEUE.spad" 187485 187495 187768 187795) (-175 "DEGRED.spad" 187102 187116 187475 187480) (-174 "DEFINTRF.spad" 184684 184694 187092 187097) (-173 "DEFINTEF.spad" 183222 183238 184674 184679) (-172 "DEFAST.spad" 182606 182614 183212 183217) (-171 "DECIMAL.spad" 180835 180843 181196 181289) (-170 "DDFACT.spad" 178656 178673 180825 180830) (-169 "DBLRESP.spad" 178256 178280 178646 178651) (-168 "DBASIS.spad" 177882 177897 178246 178251) (-167 "DBASE.spad" 176546 176556 177872 177877) (-166 "DATAARY.spad" 176032 176045 176536 176541) (-165 "CYCLOTOM.spad" 175538 175546 176022 176027) (-164 "CYCLES.spad" 172330 172338 175528 175533) (-163 "CVMP.spad" 171747 171757 172320 172325) (-162 "CTRIGMNP.spad" 170247 170263 171737 171742) (-161 "CTORKIND.spad" 169850 169858 170237 170242) (-160 "CTORCAT.spad" 169091 169099 169840 169845) (-159 "CTORCAT.spad" 168330 168340 169081 169086) (-158 "CTORCALL.spad" 167919 167929 168320 168325) (-157 "CTOR.spad" 167610 167618 167909 167914) (-156 "CSTTOOLS.spad" 166855 166868 167600 167605) (-155 "CRFP.spad" 160627 160640 166845 166850) (-154 "CRCEAST.spad" 160347 160355 160617 160622) (-153 "CRAPACK.spad" 159414 159424 160337 160342) (-152 "CPMATCH.spad" 158915 158930 159336 159341) (-151 "CPIMA.spad" 158620 158639 158905 158910) (-150 "COORDSYS.spad" 153629 153639 158610 158615) (-149 "CONTOUR.spad" 153056 153064 153619 153624) (-148 "CONTFRAC.spad" 148806 148816 152958 153051) (-147 "CONDUIT.spad" 148564 148572 148796 148801) (-146 "COMRING.spad" 148238 148246 148502 148559) (-145 "COMPPROP.spad" 147756 147764 148228 148233) (-144 "COMPLPAT.spad" 147523 147538 147746 147751) (-143 "COMPLEX2.spad" 147238 147250 147513 147518) (-142 "COMPLEX.spad" 142944 142954 143188 143446) (-141 "COMPILER.spad" 142493 142501 142934 142939) (-140 "COMPFACT.spad" 142095 142109 142483 142488) (-139 "COMPCAT.spad" 140170 140180 141832 142090) (-138 "COMPCAT.spad" 137986 137998 139650 139655) (-137 "COMMUPC.spad" 137734 137752 137976 137981) (-136 "COMMONOP.spad" 137267 137275 137724 137729) (-135 "COMMAAST.spad" 137030 137038 137257 137262) (-134 "COMM.spad" 136841 136849 137020 137025) (-133 "COMBOPC.spad" 135764 135772 136831 136836) (-132 "COMBINAT.spad" 134531 134541 135754 135759) (-131 "COMBF.spad" 131953 131969 134521 134526) (-130 "COLOR.spad" 130790 130798 131943 131948) (-129 "COLONAST.spad" 130456 130464 130780 130785) (-128 "CMPLXRT.spad" 130167 130184 130446 130451) (-127 "CLLCTAST.spad" 129829 129837 130157 130162) (-126 "CLIP.spad" 125937 125945 129819 129824) (-125 "CLIF.spad" 124592 124608 125893 125932) (-124 "CLAGG.spad" 121129 121139 124582 124587) (-123 "CLAGG.spad" 117550 117562 121005 121010) (-122 "CINTSLPE.spad" 116905 116918 117540 117545) (-121 "CHVAR.spad" 115043 115065 116895 116900) (-120 "CHARZ.spad" 114958 114966 115023 115038) (-119 "CHARPOL.spad" 114484 114494 114948 114953) (-118 "CHARNZ.spad" 114246 114254 114464 114479) (-117 "CHAR.spad" 111614 111622 114236 114241) (-116 "CFCAT.spad" 110942 110950 111604 111609) (-115 "CDEN.spad" 110162 110176 110932 110937) (-114 "CCLASS.spad" 108342 108350 109604 109643) (-113 "CATEGORY.spad" 107416 107424 108332 108337) (-112 "CATCTOR.spad" 107307 107315 107406 107411) (-111 "CATAST.spad" 106933 106941 107297 107302) (-110 "CASEAST.spad" 106647 106655 106923 106928) (-109 "CARTEN2.spad" 106037 106064 106637 106642) (-108 "CARTEN.spad" 101789 101813 106027 106032) (-107 "CARD.spad" 99084 99092 101763 101784) (-106 "CAPSLAST.spad" 98866 98874 99074 99079) (-105 "CACHSET.spad" 98490 98498 98856 98861) (-104 "CABMON.spad" 98045 98053 98480 98485) (-103 "BYTEORD.spad" 97720 97728 98035 98040) (-102 "BYTEBUF.spad" 95767 95775 96973 97000) (-101 "BYTE.spad" 95242 95250 95757 95762) (-100 "BTREE.spad" 94380 94390 94914 94941) (-99 "BTOURN.spad" 93451 93460 94052 94079) (-98 "BTCAT.spad" 93009 93018 93419 93446) (-97 "BTCAT.spad" 92587 92598 92999 93004) (-96 "BTAGG.spad" 92054 92061 92555 92582) (-95 "BTAGG.spad" 91541 91550 92044 92049) (-94 "BSTREE.spad" 90348 90357 91213 91240) (-93 "BRILL.spad" 88554 88564 90338 90343) (-92 "BRAGG.spad" 87511 87520 88544 88549) (-91 "BRAGG.spad" 86432 86443 87467 87472) (-90 "BPADICRT.spad" 84492 84503 84738 84831) (-89 "BPADIC.spad" 84165 84176 84418 84487) (-88 "BOUNDZRO.spad" 83822 83838 84155 84160) (-87 "BOP1.spad" 81281 81290 83812 83817) (-86 "BOP.spad" 76424 76431 81271 81276) (-85 "BOOLEAN.spad" 75973 75980 76414 76419) (-84 "BOOLE.spad" 75624 75631 75963 75968) (-83 "BOOLE.spad" 75273 75282 75614 75619) (-82 "BMODULE.spad" 74986 74997 75241 75268) (-81 "BITS.spad" 74418 74425 74632 74659) (-80 "catdef.spad" 74301 74311 74408 74413) (-79 "catdef.spad" 74052 74062 74291 74296) (-78 "BINDING.spad" 73474 73481 74042 74047) (-77 "BINARY.spad" 71709 71716 72064 72157) (-76 "BGAGG.spad" 71029 71038 71689 71704) (-75 "BGAGG.spad" 70357 70368 71019 71024) (-74 "BEZOUT.spad" 69498 69524 70307 70312) (-73 "BBTREE.spad" 66441 66450 69170 69197) (-72 "BASTYPE.spad" 65941 65948 66431 66436) (-71 "BASTYPE.spad" 65439 65448 65931 65936) (-70 "BALFACT.spad" 64899 64911 65429 65434) (-69 "AUTOMOR.spad" 64350 64359 64879 64894) (-68 "ATTREG.spad" 61336 61343 64114 64345) (-67 "ATTRAST.spad" 61053 61060 61326 61331) (-66 "ATRIG.spad" 60523 60530 61043 61048) (-65 "ATRIG.spad" 59991 60000 60513 60518) (-64 "ASTCAT.spad" 59895 59902 59981 59986) (-63 "ASTCAT.spad" 59797 59806 59885 59890) (-62 "ASTACK.spad" 59201 59210 59469 59496) (-61 "ASSOCEQ.spad" 58035 58046 59157 59162) (-60 "ARRAY2.spad" 57558 57567 57707 57734) (-59 "ARRAY12.spad" 56271 56282 57548 57553) (-58 "ARRAY1.spad" 55150 55159 55496 55523) (-57 "ARR2CAT.spad" 51190 51211 55118 55145) (-56 "ARR2CAT.spad" 47250 47273 51180 51185) (-55 "ARITY.spad" 46622 46629 47240 47245) (-54 "APPRULE.spad" 45906 45928 46612 46617) (-53 "APPLYORE.spad" 45525 45538 45896 45901) (-52 "ANY1.spad" 44596 44605 45515 45520) (-51 "ANY.spad" 43447 43454 44586 44591) (-50 "ANTISYM.spad" 41892 41908 43427 43442) (-49 "ANON.spad" 41601 41608 41882 41887) (-48 "AN.spad" 40069 40076 41432 41525) (-47 "AMR.spad" 38254 38265 39967 40064) (-46 "AMR.spad" 36302 36315 38017 38022) (-45 "ALIST.spad" 33540 33561 33890 33917) (-44 "ALGSC.spad" 32675 32701 33412 33465) (-43 "ALGPKG.spad" 28458 28469 32631 32636) (-42 "ALGMFACT.spad" 27651 27665 28448 28453) (-41 "ALGMANIP.spad" 25152 25167 27495 27500) (-40 "ALGFF.spad" 22970 22997 23187 23343) (-39 "ALGFACT.spad" 22089 22099 22960 22965) (-38 "ALGEBRA.spad" 21922 21931 22045 22084) (-37 "ALGEBRA.spad" 21787 21798 21912 21917) (-36 "ALAGG.spad" 21303 21324 21755 21782) (-35 "AHYP.spad" 20684 20691 21293 21298) (-34 "AGG.spad" 19393 19400 20674 20679) (-33 "AGG.spad" 18066 18075 19349 19354) (-32 "AF.spad" 16511 16526 18015 18020) (-31 "ADDAST.spad" 16197 16204 16501 16506) (-30 "ACPLOT.spad" 15074 15081 16187 16192) (-29 "ACFS.spad" 12931 12940 14976 15069) (-28 "ACFS.spad" 10874 10885 12921 12926) (-27 "ACF.spad" 7628 7635 10776 10869) (-26 "ACF.spad" 4468 4477 7618 7623) (-25 "ABELSG.spad" 4009 4016 4458 4463) (-24 "ABELSG.spad" 3548 3557 3999 4004) (-23 "ABELMON.spad" 2976 2983 3538 3543) (-22 "ABELMON.spad" 2402 2411 2966 2971) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 1962282 1962287 1962292 1962297) (-2 NIL 1962262 1962267 1962272 1962277) (-1 NIL 1962242 1962247 1962252 1962257) (0 NIL 1962222 1962227 1962232 1962237) (-1210 "ZMOD.spad" 1962031 1962044 1962160 1962217) (-1209 "ZLINDEP.spad" 1961129 1961140 1962021 1962026) (-1208 "ZDSOLVE.spad" 1951090 1951112 1961119 1961124) (-1207 "YSTREAM.spad" 1950585 1950596 1951080 1951085) (-1206 "YDIAGRAM.spad" 1950219 1950228 1950575 1950580) (-1205 "XRPOLY.spad" 1949439 1949459 1950075 1950144) (-1204 "XPR.spad" 1947234 1947247 1949157 1949256) (-1203 "XPOLYC.spad" 1946553 1946569 1947160 1947229) (-1202 "XPOLY.spad" 1946108 1946119 1946409 1946478) (-1201 "XPBWPOLY.spad" 1944579 1944599 1945914 1945983) (-1200 "XFALG.spad" 1941627 1941643 1944505 1944574) (-1199 "XF.spad" 1940090 1940105 1941529 1941622) (-1198 "XF.spad" 1938533 1938550 1939974 1939979) (-1197 "XEXPPKG.spad" 1937792 1937818 1938523 1938528) (-1196 "XDPOLY.spad" 1937406 1937422 1937648 1937717) (-1195 "XALG.spad" 1937074 1937085 1937362 1937401) (-1194 "WUTSET.spad" 1933077 1933094 1936708 1936735) (-1193 "WP.spad" 1932284 1932328 1932935 1933002) (-1192 "WHILEAST.spad" 1932082 1932091 1932274 1932279) (-1191 "WHEREAST.spad" 1931753 1931762 1932072 1932077) (-1190 "WFFINTBS.spad" 1929416 1929438 1931743 1931748) (-1189 "WEIER.spad" 1927638 1927649 1929406 1929411) (-1188 "VSPACE.spad" 1927311 1927322 1927606 1927633) (-1187 "VSPACE.spad" 1927004 1927017 1927301 1927306) (-1186 "VOID.spad" 1926681 1926690 1926994 1926999) (-1185 "VIEWDEF.spad" 1921882 1921891 1926671 1926676) (-1184 "VIEW3D.spad" 1905843 1905852 1921872 1921877) (-1183 "VIEW2D.spad" 1893742 1893751 1905833 1905838) (-1182 "VIEW.spad" 1891462 1891471 1893732 1893737) (-1181 "VECTOR2.spad" 1890101 1890114 1891452 1891457) (-1180 "VECTOR.spad" 1888820 1888831 1889071 1889098) (-1179 "VECTCAT.spad" 1886732 1886743 1888788 1888815) (-1178 "VECTCAT.spad" 1884453 1884466 1886511 1886516) (-1177 "VARIABLE.spad" 1884233 1884248 1884443 1884448) (-1176 "UTYPE.spad" 1883877 1883886 1884223 1884228) (-1175 "UTSODETL.spad" 1883172 1883196 1883833 1883838) (-1174 "UTSODE.spad" 1881388 1881408 1883162 1883167) (-1173 "UTSCAT.spad" 1878867 1878883 1881286 1881383) (-1172 "UTSCAT.spad" 1876014 1876032 1878435 1878440) (-1171 "UTS2.spad" 1875609 1875644 1876004 1876009) (-1170 "UTS.spad" 1870621 1870649 1874141 1874238) (-1169 "URAGG.spad" 1865342 1865353 1870611 1870616) (-1168 "URAGG.spad" 1860027 1860040 1865298 1865303) (-1167 "UPXSSING.spad" 1857795 1857821 1859231 1859364) (-1166 "UPXSCONS.spad" 1855613 1855633 1855986 1856135) (-1165 "UPXSCCA.spad" 1854184 1854204 1855459 1855608) (-1164 "UPXSCCA.spad" 1852897 1852919 1854174 1854179) (-1163 "UPXSCAT.spad" 1851486 1851502 1852743 1852892) (-1162 "UPXS2.spad" 1851029 1851082 1851476 1851481) (-1161 "UPXS.spad" 1848384 1848412 1849220 1849369) (-1160 "UPSQFREE.spad" 1846799 1846813 1848374 1848379) (-1159 "UPSCAT.spad" 1844594 1844618 1846697 1846794) (-1158 "UPSCAT.spad" 1842090 1842116 1844195 1844200) (-1157 "UPOLYC2.spad" 1841561 1841580 1842080 1842085) (-1156 "UPOLYC.spad" 1836641 1836652 1841403 1841556) (-1155 "UPOLYC.spad" 1831639 1831652 1836403 1836408) (-1154 "UPMP.spad" 1830571 1830584 1831629 1831634) (-1153 "UPDIVP.spad" 1830136 1830150 1830561 1830566) (-1152 "UPDECOMP.spad" 1828397 1828411 1830126 1830131) (-1151 "UPCDEN.spad" 1827614 1827630 1828387 1828392) (-1150 "UP2.spad" 1826978 1826999 1827604 1827609) (-1149 "UP.spad" 1824448 1824463 1824835 1824988) (-1148 "UNISEG2.spad" 1823945 1823958 1824404 1824409) (-1147 "UNISEG.spad" 1823298 1823309 1823864 1823869) (-1146 "UNIFACT.spad" 1822401 1822413 1823288 1823293) (-1145 "ULSCONS.spad" 1816247 1816267 1816617 1816766) (-1144 "ULSCCAT.spad" 1813984 1814004 1816093 1816242) (-1143 "ULSCCAT.spad" 1811829 1811851 1813940 1813945) (-1142 "ULSCAT.spad" 1810069 1810085 1811675 1811824) (-1141 "ULS2.spad" 1809583 1809636 1810059 1810064) (-1140 "ULS.spad" 1801616 1801644 1802561 1802984) (-1139 "UINT8.spad" 1801493 1801502 1801606 1801611) (-1138 "UINT64.spad" 1801369 1801378 1801483 1801488) (-1137 "UINT32.spad" 1801245 1801254 1801359 1801364) (-1136 "UINT16.spad" 1801121 1801130 1801235 1801240) (-1135 "UFD.spad" 1800186 1800195 1801047 1801116) (-1134 "UFD.spad" 1799313 1799324 1800176 1800181) (-1133 "UDVO.spad" 1798194 1798203 1799303 1799308) (-1132 "UDPO.spad" 1795775 1795786 1798150 1798155) (-1131 "TYPEAST.spad" 1795694 1795703 1795765 1795770) (-1130 "TYPE.spad" 1795626 1795635 1795684 1795689) (-1129 "TWOFACT.spad" 1794278 1794293 1795616 1795621) (-1128 "TUPLE.spad" 1793785 1793796 1794190 1794195) (-1127 "TUBETOOL.spad" 1790652 1790661 1793775 1793780) (-1126 "TUBE.spad" 1789299 1789316 1790642 1790647) (-1125 "TSETCAT.spad" 1777370 1777387 1789267 1789294) (-1124 "TSETCAT.spad" 1765427 1765446 1777326 1777331) (-1123 "TS.spad" 1764055 1764071 1765021 1765118) (-1122 "TRMANIP.spad" 1758419 1758436 1763743 1763748) (-1121 "TRIMAT.spad" 1757382 1757407 1758409 1758414) (-1120 "TRIGMNIP.spad" 1755909 1755926 1757372 1757377) (-1119 "TRIGCAT.spad" 1755421 1755430 1755899 1755904) (-1118 "TRIGCAT.spad" 1754931 1754942 1755411 1755416) (-1117 "TREE.spad" 1753571 1753582 1754603 1754630) (-1116 "TRANFUN.spad" 1753410 1753419 1753561 1753566) (-1115 "TRANFUN.spad" 1753247 1753258 1753400 1753405) (-1114 "TOPSP.spad" 1752921 1752930 1753237 1753242) (-1113 "TOOLSIGN.spad" 1752584 1752595 1752911 1752916) (-1112 "TEXTFILE.spad" 1751145 1751154 1752574 1752579) (-1111 "TEX1.spad" 1750701 1750712 1751135 1751140) (-1110 "TEX.spad" 1747895 1747904 1750691 1750696) (-1109 "TBCMPPK.spad" 1745996 1746019 1747885 1747890) (-1108 "TBAGG.spad" 1745239 1745262 1745964 1745991) (-1107 "TBAGG.spad" 1744502 1744527 1745229 1745234) (-1106 "TANEXP.spad" 1743910 1743921 1744492 1744497) (-1105 "TALGOP.spad" 1743634 1743645 1743900 1743905) (-1104 "TABLEAU.spad" 1743115 1743126 1743624 1743629) (-1103 "TABLE.spad" 1741390 1741413 1741660 1741687) (-1102 "TABLBUMP.spad" 1738169 1738180 1741380 1741385) (-1101 "SYSTEM.spad" 1737397 1737406 1738159 1738164) (-1100 "SYSSOLP.spad" 1734880 1734891 1737387 1737392) (-1099 "SYSPTR.spad" 1734779 1734788 1734870 1734875) (-1098 "SYSNNI.spad" 1734002 1734013 1734769 1734774) (-1097 "SYSINT.spad" 1733406 1733417 1733992 1733997) (-1096 "SYNTAX.spad" 1729740 1729749 1733396 1733401) (-1095 "SYMTAB.spad" 1727808 1727817 1729730 1729735) (-1094 "SYMS.spad" 1723837 1723846 1727798 1727803) (-1093 "SYMPOLY.spad" 1722970 1722981 1723052 1723179) (-1092 "SYMFUNC.spad" 1722471 1722482 1722960 1722965) (-1091 "SYMBOL.spad" 1719966 1719975 1722461 1722466) (-1090 "SUTS.spad" 1717079 1717107 1718498 1718595) (-1089 "SUPXS.spad" 1714421 1714449 1715270 1715419) (-1088 "SUPFRACF.spad" 1713526 1713544 1714411 1714416) (-1087 "SUP2.spad" 1712918 1712931 1713516 1713521) (-1086 "SUP.spad" 1710002 1710013 1710775 1710928) (-1085 "SUMRF.spad" 1708976 1708987 1709992 1709997) (-1084 "SUMFS.spad" 1708605 1708622 1708966 1708971) (-1083 "SULS.spad" 1700625 1700653 1701583 1702006) (-1082 "syntax.spad" 1700394 1700403 1700615 1700620) (-1081 "SUCH.spad" 1700084 1700099 1700384 1700389) (-1080 "SUBSPACE.spad" 1692215 1692230 1700074 1700079) (-1079 "SUBRESP.spad" 1691385 1691399 1692171 1692176) (-1078 "STTFNC.spad" 1687853 1687869 1691375 1691380) (-1077 "STTF.spad" 1683952 1683968 1687843 1687848) (-1076 "STTAYLOR.spad" 1676629 1676640 1683859 1683864) (-1075 "STRTBL.spad" 1675016 1675033 1675165 1675192) (-1074 "STRING.spad" 1673884 1673893 1674269 1674296) (-1073 "STREAM3.spad" 1673457 1673472 1673874 1673879) (-1072 "STREAM2.spad" 1672585 1672598 1673447 1673452) (-1071 "STREAM1.spad" 1672291 1672302 1672575 1672580) (-1070 "STREAM.spad" 1669287 1669298 1671894 1671909) (-1069 "STINPROD.spad" 1668223 1668239 1669277 1669282) (-1068 "STEPAST.spad" 1667457 1667466 1668213 1668218) (-1067 "STEP.spad" 1666774 1666783 1667447 1667452) (-1066 "STBL.spad" 1665152 1665180 1665319 1665346) (-1065 "STAGG.spad" 1663851 1663862 1665142 1665147) (-1064 "STAGG.spad" 1662548 1662561 1663841 1663846) (-1063 "STACK.spad" 1661970 1661981 1662220 1662247) (-1062 "SRING.spad" 1661730 1661739 1661960 1661965) (-1061 "SREGSET.spad" 1659462 1659479 1661364 1661391) (-1060 "SRDCMPK.spad" 1658039 1658059 1659452 1659457) (-1059 "SRAGG.spad" 1653222 1653231 1658007 1658034) (-1058 "SRAGG.spad" 1648425 1648436 1653212 1653217) (-1057 "SQMATRIX.spad" 1646102 1646120 1647018 1647105) (-1056 "SPLTREE.spad" 1640844 1640857 1645640 1645667) (-1055 "SPLNODE.spad" 1637464 1637477 1640834 1640839) (-1054 "SPFCAT.spad" 1636273 1636282 1637454 1637459) (-1053 "SPECOUT.spad" 1634825 1634834 1636263 1636268) (-1052 "SPADXPT.spad" 1626916 1626925 1634815 1634820) (-1051 "spad-parser.spad" 1626381 1626390 1626906 1626911) (-1050 "SPADAST.spad" 1626082 1626091 1626371 1626376) (-1049 "SPACEC.spad" 1610297 1610308 1626072 1626077) (-1048 "SPACE3.spad" 1610073 1610084 1610287 1610292) (-1047 "SORTPAK.spad" 1609622 1609635 1610029 1610034) (-1046 "SOLVETRA.spad" 1607385 1607396 1609612 1609617) (-1045 "SOLVESER.spad" 1605841 1605852 1607375 1607380) (-1044 "SOLVERAD.spad" 1601867 1601878 1605831 1605836) (-1043 "SOLVEFOR.spad" 1600329 1600347 1601857 1601862) (-1042 "SNTSCAT.spad" 1599929 1599946 1600297 1600324) (-1041 "SMTS.spad" 1598246 1598272 1599523 1599620) (-1040 "SMP.spad" 1596054 1596074 1596444 1596571) (-1039 "SMITH.spad" 1594899 1594924 1596044 1596049) (-1038 "SMATCAT.spad" 1593017 1593047 1594843 1594894) (-1037 "SMATCAT.spad" 1591067 1591099 1592895 1592900) (-1036 "aggcat.spad" 1590743 1590754 1591047 1591062) (-1035 "SKAGG.spad" 1589712 1589723 1590711 1590738) (-1034 "SINT.spad" 1589011 1589020 1589578 1589707) (-1033 "SIMPAN.spad" 1588739 1588748 1589001 1589006) (-1032 "SIGNRF.spad" 1587864 1587875 1588729 1588734) (-1031 "SIGNEF.spad" 1587150 1587167 1587854 1587859) (-1030 "syntax.spad" 1586567 1586576 1587140 1587145) (-1029 "SIG.spad" 1585929 1585938 1586557 1586562) (-1028 "SHP.spad" 1583873 1583888 1585885 1585890) (-1027 "SHDP.spad" 1573366 1573393 1573883 1573980) (-1026 "SGROUP.spad" 1572974 1572983 1573356 1573361) (-1025 "SGROUP.spad" 1572580 1572591 1572964 1572969) (-1024 "catdef.spad" 1572290 1572302 1572401 1572575) (-1023 "catdef.spad" 1571846 1571858 1572111 1572285) (-1022 "SGCF.spad" 1564985 1564994 1571836 1571841) (-1021 "SFRTCAT.spad" 1563931 1563948 1564953 1564980) (-1020 "SFRGCD.spad" 1562994 1563014 1563921 1563926) (-1019 "SFQCMPK.spad" 1557807 1557827 1562984 1562989) (-1018 "SEXOF.spad" 1557650 1557690 1557797 1557802) (-1017 "SEXCAT.spad" 1555478 1555518 1557640 1557645) (-1016 "SEX.spad" 1555370 1555379 1555468 1555473) (-1015 "SETMN.spad" 1553830 1553847 1555360 1555365) (-1014 "SETCAT.spad" 1553315 1553324 1553820 1553825) (-1013 "SETCAT.spad" 1552798 1552809 1553305 1553310) (-1012 "SETAGG.spad" 1549347 1549358 1552778 1552793) (-1011 "SETAGG.spad" 1545904 1545917 1549337 1549342) (-1010 "SET.spad" 1544213 1544224 1545310 1545349) (-1009 "syntax.spad" 1543916 1543925 1544203 1544208) (-1008 "SEGXCAT.spad" 1543072 1543085 1543906 1543911) (-1007 "SEGCAT.spad" 1541997 1542008 1543062 1543067) (-1006 "SEGBIND2.spad" 1541695 1541708 1541987 1541992) (-1005 "SEGBIND.spad" 1541453 1541464 1541642 1541647) (-1004 "SEGAST.spad" 1541183 1541192 1541443 1541448) (-1003 "SEG2.spad" 1540618 1540631 1541139 1541144) (-1002 "SEG.spad" 1540431 1540442 1540537 1540542) (-1001 "SDVAR.spad" 1539707 1539718 1540421 1540426) (-1000 "SDPOL.spad" 1537399 1537410 1537690 1537817) (-999 "SCPKG.spad" 1535489 1535499 1537389 1537394) (-998 "SCOPE.spad" 1534667 1534675 1535479 1535484) (-997 "SCACHE.spad" 1533364 1533374 1534657 1534662) (-996 "SASTCAT.spad" 1533274 1533282 1533354 1533359) (-995 "SAOS.spad" 1533147 1533155 1533264 1533269) (-994 "SAERFFC.spad" 1532861 1532880 1533137 1533142) (-993 "SAEFACT.spad" 1532563 1532582 1532851 1532856) (-992 "SAE.spad" 1530214 1530229 1530824 1530959) (-991 "RURPK.spad" 1527874 1527889 1530204 1530209) (-990 "RULESET.spad" 1527328 1527351 1527864 1527869) (-989 "RULECOLD.spad" 1527181 1527193 1527318 1527323) (-988 "RULE.spad" 1525430 1525453 1527171 1527176) (-987 "RTVALUE.spad" 1525166 1525174 1525420 1525425) (-986 "syntax.spad" 1524884 1524892 1525156 1525161) (-985 "RSETGCD.spad" 1521327 1521346 1524874 1524879) (-984 "RSETCAT.spad" 1511296 1511312 1521295 1521322) (-983 "RSETCAT.spad" 1501285 1501303 1511286 1511291) (-982 "RSDCMPK.spad" 1499786 1499805 1501275 1501280) (-981 "RRCC.spad" 1498171 1498200 1499776 1499781) (-980 "RRCC.spad" 1496554 1496585 1498161 1498166) (-979 "RPTAST.spad" 1496257 1496265 1496544 1496549) (-978 "RPOLCAT.spad" 1475762 1475776 1496125 1496252) (-977 "RPOLCAT.spad" 1455060 1455076 1475425 1475430) (-976 "ROMAN.spad" 1454389 1454397 1454926 1455055) (-975 "ROIRC.spad" 1453470 1453501 1454379 1454384) (-974 "RNS.spad" 1452447 1452455 1453372 1453465) (-973 "RNS.spad" 1451510 1451520 1452437 1452442) (-972 "RNGBIND.spad" 1450671 1450684 1451465 1451470) (-971 "RNG.spad" 1450280 1450288 1450661 1450666) (-970 "RNG.spad" 1449887 1449897 1450270 1450275) (-969 "RMODULE.spad" 1449669 1449679 1449877 1449882) (-968 "RMCAT2.spad" 1449090 1449146 1449659 1449664) (-967 "RMATRIX.spad" 1447900 1447918 1448242 1448281) (-966 "RMATCAT.spad" 1443538 1443568 1447856 1447895) (-965 "RMATCAT.spad" 1439066 1439098 1443386 1443391) (-964 "RLINSET.spad" 1438771 1438781 1439056 1439061) (-963 "RINTERP.spad" 1438660 1438679 1438761 1438766) (-962 "RING.spad" 1438131 1438139 1438640 1438655) (-961 "RING.spad" 1437610 1437620 1438121 1438126) (-960 "RIDIST.spad" 1437003 1437011 1437600 1437605) (-959 "RGCHAIN.spad" 1435558 1435573 1436451 1436478) (-958 "RGBCSPC.spad" 1435348 1435359 1435548 1435553) (-957 "RGBCMDL.spad" 1434911 1434922 1435338 1435343) (-956 "RFFACTOR.spad" 1434374 1434384 1434901 1434906) (-955 "RFFACT.spad" 1434110 1434121 1434364 1434369) (-954 "RFDIST.spad" 1433107 1433115 1434100 1434105) (-953 "RF.spad" 1430782 1430792 1433097 1433102) (-952 "RETSOL.spad" 1430202 1430214 1430772 1430777) (-951 "RETRACT.spad" 1429631 1429641 1430192 1430197) (-950 "RETRACT.spad" 1429058 1429070 1429621 1429626) (-949 "RETAST.spad" 1428871 1428879 1429048 1429053) (-948 "RESRING.spad" 1428219 1428265 1428809 1428866) (-947 "RESLATC.spad" 1427544 1427554 1428209 1428214) (-946 "REPSQ.spad" 1427276 1427286 1427534 1427539) (-945 "REPDB.spad" 1426984 1426994 1427266 1427271) (-944 "REP2.spad" 1416699 1416709 1426826 1426831) (-943 "REP1.spad" 1410920 1410930 1416649 1416654) (-942 "REP.spad" 1408475 1408483 1410910 1410915) (-941 "REGSET.spad" 1406301 1406317 1408109 1408136) (-940 "REF.spad" 1405820 1405830 1406291 1406296) (-939 "REDORDER.spad" 1405027 1405043 1405810 1405815) (-938 "RECLOS.spad" 1403924 1403943 1404627 1404720) (-937 "REALSOLV.spad" 1403065 1403073 1403914 1403919) (-936 "REAL0Q.spad" 1400364 1400378 1403055 1403060) (-935 "REAL0.spad" 1397209 1397223 1400354 1400359) (-934 "REAL.spad" 1397082 1397090 1397199 1397204) (-933 "RDUCEAST.spad" 1396804 1396812 1397072 1397077) (-932 "RDIV.spad" 1396460 1396484 1396794 1396799) (-931 "RDIST.spad" 1396028 1396038 1396450 1396455) (-930 "RDETRS.spad" 1394893 1394910 1396018 1396023) (-929 "RDETR.spad" 1393033 1393050 1394883 1394888) (-928 "RDEEFS.spad" 1392133 1392149 1393023 1393028) (-927 "RDEEF.spad" 1391144 1391160 1392123 1392128) (-926 "RCFIELD.spad" 1388363 1388371 1391046 1391139) (-925 "RCFIELD.spad" 1385668 1385678 1388353 1388358) (-924 "RCAGG.spad" 1383605 1383615 1385658 1385663) (-923 "RCAGG.spad" 1381471 1381483 1383526 1383531) (-922 "RATRET.spad" 1380832 1380842 1381461 1381466) (-921 "RATFACT.spad" 1380525 1380536 1380822 1380827) (-920 "RANDSRC.spad" 1379845 1379853 1380515 1380520) (-919 "RADUTIL.spad" 1379602 1379610 1379835 1379840) (-918 "RADIX.spad" 1376647 1376660 1378192 1378285) (-917 "RADFF.spad" 1374564 1374600 1374682 1374838) (-916 "RADCAT.spad" 1374160 1374168 1374554 1374559) (-915 "RADCAT.spad" 1373754 1373764 1374150 1374155) (-914 "QUEUE.spad" 1373168 1373178 1373426 1373453) (-913 "QUATCT2.spad" 1372789 1372807 1373158 1373163) (-912 "QUATCAT.spad" 1370960 1370970 1372719 1372784) (-911 "QUATCAT.spad" 1368896 1368908 1370657 1370662) (-910 "QUAT.spad" 1367503 1367513 1367845 1367910) (-909 "QUAGG.spad" 1366337 1366347 1367471 1367498) (-908 "QQUTAST.spad" 1366106 1366114 1366327 1366332) (-907 "QFORM.spad" 1365725 1365739 1366096 1366101) (-906 "QFCAT2.spad" 1365418 1365434 1365715 1365720) (-905 "QFCAT.spad" 1364121 1364131 1365320 1365413) (-904 "QFCAT.spad" 1362457 1362469 1363658 1363663) (-903 "QEQUAT.spad" 1362016 1362024 1362447 1362452) (-902 "QCMPACK.spad" 1356931 1356950 1362006 1362011) (-901 "QALGSET2.spad" 1354927 1354945 1356921 1356926) (-900 "QALGSET.spad" 1351032 1351064 1354841 1354846) (-899 "PWFFINTB.spad" 1348448 1348469 1351022 1351027) (-898 "PUSHVAR.spad" 1347787 1347806 1348438 1348443) (-897 "PTRANFN.spad" 1343923 1343933 1347777 1347782) (-896 "PTPACK.spad" 1341011 1341021 1343913 1343918) (-895 "PTFUNC2.spad" 1340834 1340848 1341001 1341006) (-894 "PTCAT.spad" 1340089 1340099 1340802 1340829) (-893 "PSQFR.spad" 1339404 1339428 1340079 1340084) (-892 "PSEUDLIN.spad" 1338290 1338300 1339394 1339399) (-891 "PSETPK.spad" 1324995 1325011 1338168 1338173) (-890 "PSETCAT.spad" 1319395 1319418 1324975 1324990) (-889 "PSETCAT.spad" 1313769 1313794 1319351 1319356) (-888 "PSCURVE.spad" 1312768 1312776 1313759 1313764) (-887 "PSCAT.spad" 1311551 1311580 1312666 1312763) (-886 "PSCAT.spad" 1310424 1310455 1311541 1311546) (-885 "PRTITION.spad" 1309122 1309130 1310414 1310419) (-884 "PRTDAST.spad" 1308841 1308849 1309112 1309117) (-883 "PRS.spad" 1298459 1298476 1308797 1308802) (-882 "PRQAGG.spad" 1297894 1297904 1298427 1298454) (-881 "PROPLOG.spad" 1297498 1297506 1297884 1297889) (-880 "PROPFUN2.spad" 1297121 1297134 1297488 1297493) (-879 "PROPFUN1.spad" 1296527 1296538 1297111 1297116) (-878 "PROPFRML.spad" 1295095 1295106 1296517 1296522) (-877 "PROPERTY.spad" 1294591 1294599 1295085 1295090) (-876 "PRODUCT.spad" 1292288 1292300 1292572 1292627) (-875 "PRINT.spad" 1292040 1292048 1292278 1292283) (-874 "PRIMES.spad" 1290301 1290311 1292030 1292035) (-873 "PRIMELT.spad" 1288422 1288436 1290291 1290296) (-872 "PRIMCAT.spad" 1288065 1288073 1288412 1288417) (-871 "PRIMARR2.spad" 1286832 1286844 1288055 1288060) (-870 "PRIMARR.spad" 1285887 1285897 1286057 1286084) (-869 "PREASSOC.spad" 1285269 1285281 1285877 1285882) (-868 "PR.spad" 1283787 1283799 1284486 1284613) (-867 "PPCURVE.spad" 1282924 1282932 1283777 1283782) (-866 "PORTNUM.spad" 1282715 1282723 1282914 1282919) (-865 "POLYROOT.spad" 1281564 1281586 1282671 1282676) (-864 "POLYLIFT.spad" 1280829 1280852 1281554 1281559) (-863 "POLYCATQ.spad" 1278955 1278977 1280819 1280824) (-862 "POLYCAT.spad" 1272457 1272478 1278823 1278950) (-861 "POLYCAT.spad" 1265479 1265502 1271847 1271852) (-860 "POLY2UP.spad" 1264931 1264945 1265469 1265474) (-859 "POLY2.spad" 1264528 1264540 1264921 1264926) (-858 "POLY.spad" 1262196 1262206 1262711 1262838) (-857 "POLUTIL.spad" 1261161 1261190 1262152 1262157) (-856 "POLTOPOL.spad" 1259909 1259924 1261151 1261156) (-855 "POINT.spad" 1258792 1258802 1258879 1258906) (-854 "PNTHEORY.spad" 1255494 1255502 1258782 1258787) (-853 "PMTOOLS.spad" 1254269 1254283 1255484 1255489) (-852 "PMSYM.spad" 1253818 1253828 1254259 1254264) (-851 "PMQFCAT.spad" 1253409 1253423 1253808 1253813) (-850 "PMPREDFS.spad" 1252871 1252893 1253399 1253404) (-849 "PMPRED.spad" 1252358 1252372 1252861 1252866) (-848 "PMPLCAT.spad" 1251435 1251453 1252287 1252292) (-847 "PMLSAGG.spad" 1251020 1251034 1251425 1251430) (-846 "PMKERNEL.spad" 1250599 1250611 1251010 1251015) (-845 "PMINS.spad" 1250179 1250189 1250589 1250594) (-844 "PMFS.spad" 1249756 1249774 1250169 1250174) (-843 "PMDOWN.spad" 1249046 1249060 1249746 1249751) (-842 "PMASSFS.spad" 1248021 1248037 1249036 1249041) (-841 "PMASS.spad" 1247039 1247047 1248011 1248016) (-840 "PLOTTOOL.spad" 1246819 1246827 1247029 1247034) (-839 "PLOT3D.spad" 1243283 1243291 1246809 1246814) (-838 "PLOT1.spad" 1242456 1242466 1243273 1243278) (-837 "PLOT.spad" 1237379 1237387 1242446 1242451) (-836 "PLEQN.spad" 1224781 1224808 1237369 1237374) (-835 "PINTERPA.spad" 1224565 1224581 1224771 1224776) (-834 "PINTERP.spad" 1224187 1224206 1224555 1224560) (-833 "PID.spad" 1223161 1223169 1224113 1224182) (-832 "PICOERCE.spad" 1222818 1222828 1223151 1223156) (-831 "PI.spad" 1222435 1222443 1222792 1222813) (-830 "PGROEB.spad" 1221044 1221058 1222425 1222430) (-829 "PGE.spad" 1212717 1212725 1221034 1221039) (-828 "PGCD.spad" 1211671 1211688 1212707 1212712) (-827 "PFRPAC.spad" 1210820 1210830 1211661 1211666) (-826 "PFR.spad" 1207523 1207533 1210722 1210815) (-825 "PFOTOOLS.spad" 1206781 1206797 1207513 1207518) (-824 "PFOQ.spad" 1206151 1206169 1206771 1206776) (-823 "PFO.spad" 1205570 1205597 1206141 1206146) (-822 "PFECAT.spad" 1203280 1203288 1205496 1205565) (-821 "PFECAT.spad" 1201018 1201028 1203236 1203241) (-820 "PFBRU.spad" 1198906 1198918 1201008 1201013) (-819 "PFBR.spad" 1196466 1196489 1198896 1198901) (-818 "PF.spad" 1196040 1196052 1196271 1196364) (-817 "PERMGRP.spad" 1190810 1190820 1196030 1196035) (-816 "PERMCAT.spad" 1189471 1189481 1190790 1190805) (-815 "PERMAN.spad" 1188027 1188041 1189461 1189466) (-814 "PERM.spad" 1183837 1183847 1187860 1187875) (-813 "PENDTREE.spad" 1183251 1183261 1183531 1183536) (-812 "PDSPC.spad" 1182064 1182074 1183241 1183246) (-811 "PDSPC.spad" 1180875 1180887 1182054 1182059) (-810 "PDRING.spad" 1180717 1180727 1180855 1180870) (-809 "PDMOD.spad" 1180533 1180545 1180685 1180712) (-808 "PDECOMP.spad" 1180003 1180020 1180523 1180528) (-807 "PDDOM.spad" 1179441 1179454 1179993 1179998) (-806 "PDDOM.spad" 1178877 1178892 1179431 1179436) (-805 "PCOMP.spad" 1178730 1178743 1178867 1178872) (-804 "PBWLB.spad" 1177328 1177345 1178720 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226630 227024 227075) (-200 "DIVRING.spad" 226208 226218 226612 226617) (-199 "DISPLAY.spad" 224398 224406 226198 226203) (-198 "DIRPROD2.spad" 223216 223234 224388 224393) (-197 "DIRPROD.spad" 212586 212602 213226 213323) (-196 "DIRPCAT.spad" 211869 211885 212484 212581) (-195 "DIRPCAT.spad" 210778 210796 211395 211400) (-194 "DIOSP.spad" 209603 209611 210768 210773) (-193 "DIOPS.spad" 208599 208609 209583 209598) (-192 "DIOPS.spad" 207569 207581 208555 208560) (-191 "catdef.spad" 207427 207435 207559 207564) (-190 "DIFRING.spad" 207265 207273 207407 207422) (-189 "DIFFSPC.spad" 206844 206852 207255 207260) (-188 "DIFFSPC.spad" 206421 206431 206834 206839) (-187 "DIFFMOD.spad" 205910 205920 206389 206416) (-186 "DIFFDOM.spad" 205075 205086 205900 205905) (-185 "DIFFDOM.spad" 204238 204251 205065 205070) (-184 "DIFEXT.spad" 204057 204067 204218 204233) (-183 "DIAGG.spad" 203687 203697 204037 204052) (-182 "DIAGG.spad" 203325 203337 203677 203682) (-181 "DHMATRIX.spad" 201702 201712 202847 202874) (-180 "DFSFUN.spad" 195342 195350 201692 201697) (-179 "DFLOAT.spad" 191949 191957 195232 195337) (-178 "DFINTTLS.spad" 190180 190196 191939 191944) (-177 "DERHAM.spad" 188094 188126 190160 190175) (-176 "DEQUEUE.spad" 187483 187493 187766 187793) (-175 "DEGRED.spad" 187100 187114 187473 187478) (-174 "DEFINTRF.spad" 184682 184692 187090 187095) (-173 "DEFINTEF.spad" 183220 183236 184672 184677) (-172 "DEFAST.spad" 182604 182612 183210 183215) (-171 "DECIMAL.spad" 180833 180841 181194 181287) (-170 "DDFACT.spad" 178654 178671 180823 180828) (-169 "DBLRESP.spad" 178254 178278 178644 178649) (-168 "DBASIS.spad" 177880 177895 178244 178249) (-167 "DBASE.spad" 176544 176554 177870 177875) (-166 "DATAARY.spad" 176030 176043 176534 176539) (-165 "CYCLOTOM.spad" 175536 175544 176020 176025) (-164 "CYCLES.spad" 172328 172336 175526 175531) (-163 "CVMP.spad" 171745 171755 172318 172323) (-162 "CTRIGMNP.spad" 170245 170261 171735 171740) (-161 "CTORKIND.spad" 169848 169856 170235 170240) (-160 "CTORCAT.spad" 169089 169097 169838 169843) (-159 "CTORCAT.spad" 168328 168338 169079 169084) (-158 "CTORCALL.spad" 167917 167927 168318 168323) (-157 "CTOR.spad" 167608 167616 167907 167912) (-156 "CSTTOOLS.spad" 166853 166866 167598 167603) (-155 "CRFP.spad" 160625 160638 166843 166848) (-154 "CRCEAST.spad" 160345 160353 160615 160620) (-153 "CRAPACK.spad" 159412 159422 160335 160340) (-152 "CPMATCH.spad" 158913 158928 159334 159339) (-151 "CPIMA.spad" 158618 158637 158903 158908) (-150 "COORDSYS.spad" 153627 153637 158608 158613) (-149 "CONTOUR.spad" 153054 153062 153617 153622) (-148 "CONTFRAC.spad" 148804 148814 152956 153049) (-147 "CONDUIT.spad" 148562 148570 148794 148799) (-146 "COMRING.spad" 148236 148244 148500 148557) (-145 "COMPPROP.spad" 147754 147762 148226 148231) (-144 "COMPLPAT.spad" 147521 147536 147744 147749) (-143 "COMPLEX2.spad" 147236 147248 147511 147516) (-142 "COMPLEX.spad" 142942 142952 143186 143444) (-141 "COMPILER.spad" 142491 142499 142932 142937) (-140 "COMPFACT.spad" 142093 142107 142481 142486) (-139 "COMPCAT.spad" 140168 140178 141830 142088) (-138 "COMPCAT.spad" 137984 137996 139648 139653) (-137 "COMMUPC.spad" 137732 137750 137974 137979) (-136 "COMMONOP.spad" 137265 137273 137722 137727) (-135 "COMMAAST.spad" 137028 137036 137255 137260) (-134 "COMM.spad" 136839 136847 137018 137023) (-133 "COMBOPC.spad" 135762 135770 136829 136834) (-132 "COMBINAT.spad" 134529 134539 135752 135757) (-131 "COMBF.spad" 131951 131967 134519 134524) (-130 "COLOR.spad" 130788 130796 131941 131946) (-129 "COLONAST.spad" 130454 130462 130778 130783) (-128 "CMPLXRT.spad" 130165 130182 130444 130449) (-127 "CLLCTAST.spad" 129827 129835 130155 130160) (-126 "CLIP.spad" 125935 125943 129817 129822) (-125 "CLIF.spad" 124590 124606 125891 125930) (-124 "CLAGG.spad" 121127 121137 124580 124585) (-123 "CLAGG.spad" 117550 117562 121005 121010) (-122 "CINTSLPE.spad" 116905 116918 117540 117545) (-121 "CHVAR.spad" 115043 115065 116895 116900) (-120 "CHARZ.spad" 114958 114966 115023 115038) (-119 "CHARPOL.spad" 114484 114494 114948 114953) (-118 "CHARNZ.spad" 114246 114254 114464 114479) (-117 "CHAR.spad" 111614 111622 114236 114241) (-116 "CFCAT.spad" 110942 110950 111604 111609) (-115 "CDEN.spad" 110162 110176 110932 110937) (-114 "CCLASS.spad" 108342 108350 109604 109643) (-113 "CATEGORY.spad" 107416 107424 108332 108337) (-112 "CATCTOR.spad" 107307 107315 107406 107411) (-111 "CATAST.spad" 106933 106941 107297 107302) (-110 "CASEAST.spad" 106647 106655 106923 106928) (-109 "CARTEN2.spad" 106037 106064 106637 106642) (-108 "CARTEN.spad" 101789 101813 106027 106032) (-107 "CARD.spad" 99084 99092 101763 101784) (-106 "CAPSLAST.spad" 98866 98874 99074 99079) (-105 "CACHSET.spad" 98490 98498 98856 98861) (-104 "CABMON.spad" 98045 98053 98480 98485) (-103 "BYTEORD.spad" 97720 97728 98035 98040) (-102 "BYTEBUF.spad" 95767 95775 96973 97000) (-101 "BYTE.spad" 95242 95250 95757 95762) (-100 "BTREE.spad" 94380 94390 94914 94941) (-99 "BTOURN.spad" 93451 93460 94052 94079) (-98 "BTCAT.spad" 93009 93018 93419 93446) (-97 "BTCAT.spad" 92587 92598 92999 93004) (-96 "BTAGG.spad" 92054 92061 92555 92582) (-95 "BTAGG.spad" 91541 91550 92044 92049) (-94 "BSTREE.spad" 90348 90357 91213 91240) (-93 "BRILL.spad" 88554 88564 90338 90343) (-92 "BRAGG.spad" 87511 87520 88544 88549) (-91 "BRAGG.spad" 86432 86443 87467 87472) (-90 "BPADICRT.spad" 84492 84503 84738 84831) (-89 "BPADIC.spad" 84165 84176 84418 84487) (-88 "BOUNDZRO.spad" 83822 83838 84155 84160) (-87 "BOP1.spad" 81281 81290 83812 83817) (-86 "BOP.spad" 76424 76431 81271 81276) (-85 "BOOLEAN.spad" 75973 75980 76414 76419) (-84 "BOOLE.spad" 75624 75631 75963 75968) (-83 "BOOLE.spad" 75273 75282 75614 75619) (-82 "BMODULE.spad" 74986 74997 75241 75268) (-81 "BITS.spad" 74418 74425 74632 74659) (-80 "catdef.spad" 74301 74311 74408 74413) (-79 "catdef.spad" 74052 74062 74291 74296) (-78 "BINDING.spad" 73474 73481 74042 74047) (-77 "BINARY.spad" 71709 71716 72064 72157) (-76 "BGAGG.spad" 71029 71038 71689 71704) (-75 "BGAGG.spad" 70357 70368 71019 71024) (-74 "BEZOUT.spad" 69498 69524 70307 70312) (-73 "BBTREE.spad" 66441 66450 69170 69197) (-72 "BASTYPE.spad" 65941 65948 66431 66436) (-71 "BASTYPE.spad" 65439 65448 65931 65936) (-70 "BALFACT.spad" 64899 64911 65429 65434) (-69 "AUTOMOR.spad" 64350 64359 64879 64894) (-68 "ATTREG.spad" 61336 61343 64114 64345) (-67 "ATTRAST.spad" 61053 61060 61326 61331) (-66 "ATRIG.spad" 60523 60530 61043 61048) (-65 "ATRIG.spad" 59991 60000 60513 60518) (-64 "ASTCAT.spad" 59895 59902 59981 59986) (-63 "ASTCAT.spad" 59797 59806 59885 59890) (-62 "ASTACK.spad" 59201 59210 59469 59496) (-61 "ASSOCEQ.spad" 58035 58046 59157 59162) (-60 "ARRAY2.spad" 57558 57567 57707 57734) (-59 "ARRAY12.spad" 56271 56282 57548 57553) (-58 "ARRAY1.spad" 55150 55159 55496 55523) (-57 "ARR2CAT.spad" 51190 51211 55118 55145) (-56 "ARR2CAT.spad" 47250 47273 51180 51185) (-55 "ARITY.spad" 46622 46629 47240 47245) (-54 "APPRULE.spad" 45906 45928 46612 46617) (-53 "APPLYORE.spad" 45525 45538 45896 45901) (-52 "ANY1.spad" 44596 44605 45515 45520) (-51 "ANY.spad" 43447 43454 44586 44591) (-50 "ANTISYM.spad" 41892 41908 43427 43442) (-49 "ANON.spad" 41601 41608 41882 41887) (-48 "AN.spad" 40069 40076 41432 41525) (-47 "AMR.spad" 38254 38265 39967 40064) (-46 "AMR.spad" 36302 36315 38017 38022) (-45 "ALIST.spad" 33540 33561 33890 33917) (-44 "ALGSC.spad" 32675 32701 33412 33465) (-43 "ALGPKG.spad" 28458 28469 32631 32636) (-42 "ALGMFACT.spad" 27651 27665 28448 28453) (-41 "ALGMANIP.spad" 25152 25167 27495 27500) (-40 "ALGFF.spad" 22970 22997 23187 23343) (-39 "ALGFACT.spad" 22089 22099 22960 22965) (-38 "ALGEBRA.spad" 21922 21931 22045 22084) (-37 "ALGEBRA.spad" 21787 21798 21912 21917) (-36 "ALAGG.spad" 21303 21324 21755 21782) (-35 "AHYP.spad" 20684 20691 21293 21298) (-34 "AGG.spad" 19393 19400 20674 20679) (-33 "AGG.spad" 18066 18075 19349 19354) (-32 "AF.spad" 16511 16526 18015 18020) (-31 "ADDAST.spad" 16197 16204 16501 16506) (-30 "ACPLOT.spad" 15074 15081 16187 16192) (-29 "ACFS.spad" 12931 12940 14976 15069) (-28 "ACFS.spad" 10874 10885 12921 12926) (-27 "ACF.spad" 7628 7635 10776 10869) (-26 "ACF.spad" 4468 4477 7618 7623) (-25 "ABELSG.spad" 4009 4016 4458 4463) (-24 "ABELSG.spad" 3548 3557 3999 4004) (-23 "ABELMON.spad" 2976 2983 3538 3543) (-22 "ABELMON.spad" 2402 2411 2966 2971) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
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